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Primary Maths · Year 4Chapter 6 · Decimals and money
Year 4 · Chapter 6

Year 4 Tenths, Hundredths and Money: worked examples and questions with answers

By the end of this chapter you will be able to

  • Write tenths and hundredths as fractions and as decimals, and know what each digit is worth
  • Use place-value charts, hundred squares and number lines to show decimals with up to two decimal places
  • Write 1/2, 1/4 and 3/4 as the decimals 0.5, 0.25 and 0.75
  • Count up and down in tenths and hundredths, including across a whole number
  • Divide one- and two-digit numbers by 10 and 100 by moving the digits to the right
  • Compare and order decimals, and round a decimal with one decimal place to the nearest whole number
  • Write amounts of money in pounds and pence, change between £ and p, and compare money
  • Add, subtract, multiply and share money, work out change, and solve simple measure problems with decimals

You should already know

  • Tenths and hundredths as fractions (Chapter 5)
  • Place value of whole numbers and rounding to the nearest 10 (Chapter 1)
  • Adding and subtracting with columns (Chapter 2)
  • Times tables and multiplying and dividing by 10 and 100 (Chapters 3 and 4)

Where this leads

  • Converting units of length, mass and capacity (Chapter 7)
  • Decimals with three places and percentages in Year 5
  • Adding and subtracting decimals with more digits in Year 5
  • Multiplying and dividing decimals in Year 6

National Curriculum for England, Key Stage 2 mathematics, Year 4. Content: Recognise that hundredths arise when dividing an object by 100 and dividing tenths by ten, Count up and down in hundredths; recognise and write decimal equivalents of any number of tenths or hundredths, Recognise and write decimal equivalents to 1/4, 1/2 and 3/4, Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths, Round decimals with one decimal place to the nearest whole number, Compare numbers with the same number of decimal places up to two decimal places, Solve simple measure and money problems involving fractions and decimals to two decimal places, Estimate, compare and calculate money in pounds and pence.

Printable worksheets. Every lesson in this chapter has a free worksheet and an answer sheet to download and print.

Exercise P  Do you remember?

Non-calculator
1
FWhat fraction of the bar is shaded?
2
FWork out 560 ÷ 10.
3
FHow many pence are there in £2?
4
FRound 47 to the nearest 10.
5
FWrite < or > in the box.   4,350  [ ]   4,305
6.1

Tenths as decimals

Year 4
Tenths as fractions and decimals, Counting in tenths, Decimal point and place value

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Tenths as decimalsComing soon

In Chapter 5 you cut a whole into 10 equal parts. Each part is one tenth, written 1/10. There is another way to write a tenth. We can write it as a decimal: 0.1. The dot is called the decimal point.

0.10.10.10.10.10.10.10.10.10.1
A whole cut into 10 equal parts. Each part is 0.1. Three parts are shaded: 3/10 = 0.3.

The decimal point separates the whole numbers from the parts of a whole. Digits to the left of the point are whole numbers (ones, tens...). The first digit to the right of the point is the tenths digit. So 0.3 means 0 ones and 3 tenths.

Ones10tenths0.1.1.1.13
A place-value chart for 0.3. There are 0 ones and 3 tenths. Each counter in the tenths column is worth 0.1.

On a number line. Between 0 and 1 there are 10 equal gaps. Each gap is one tenth, 0.1.

0.00.10.20.30.40.50.60.70.80.91.0A
The number line from 0 to 1 in tenths. A is at 3 tenths, so A = 0.3.

More than one. We can have whole ones and tenths. 2 and 4 tenths is the mixed number 2 4/10, and as a decimal it is 2.4. The 2 is in the ones column and the 4 is in the tenths column.

Ones1112tenths0.1.1.1.1.14
2.4 = 2 ones and 4 tenths = 2 4/10.

Counting in tenths. Count on 0.1 each time: 0.7, 0.8, 0.9, 1.0, 1.1, 1.2. Ten tenths make one whole, so 0.9 + 0.1 = 1.0. The number 1.0 is the same as 1. Counting back works the same way: 1.2, 1.1, 1.0, 0.9, 0.8.

Dividing by 10. Dividing 1 whole by 10 gives one tenth: 1 ÷ 10 = 0.1. And 3 ÷ 10 = 0.3. You will see more about this in Section 6.4.

Key words. A decimal is a number with a decimal point. Tenths are the first column after the point.

Key ideas

  • A tenth is 1 of 10 equal parts: 1/10 = 0.1.
  • The decimal point separates whole numbers (left) from parts of a whole (right).
  • The first digit after the point is the tenths digit: 0.7 is 7 tenths = 7/10.
  • 10 tenths make 1 whole: 0.9 + 0.1 = 1.0.
  • A mixed number with tenths is a decimal: 2 4/10 = 2.4.
  • Write a 0 before the point when there are no whole ones: 0.7 (not .7).
Worked example 6.1.1
What decimal is shaded?

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Count the tenths that are shaded. Tenths are the first column after the decimal point.

  1. Count the equal parts in the whole. The whole is cut into 10 equal parts. Each part is one tenth.
    There are 10 parts, so the bottom number is 10.
  2. Count the shaded parts. This gives the top number.
    7 parts are shaded, so the fraction is 710.
  3. Write it as a decimal. Tenths go in the first column after the decimal point.
    onestenths
    0.70.7

    0 ones and 7 tenths = 0.7

Check. Go back to a fraction: 0.7 has 7 in the tenths column, so it is 710. ✓

Watch out. Write the 0 ones before the decimal point: 0.7, not .7.

Worked example 6.1.2
Write 4/10 as a decimal.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Look at the bottom number: 10 means tenths and 100 means hundredths. Put the digits in a place-value table and write the decimal point after the ones.

  1. Look at the bottom number. 10 means tenths. Tenths go in the first column after the decimal point.
    410 is 4 tenths.
  2. Look at the picture.
  3. Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
    onestenths
    0.40.4
  4. Write the decimal.
    410 = 0.4

Check. Go back to a fraction: 0.4 = 410. ✓

Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.

Worked example 6.1.3
Write 2 3/10 as a decimal.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Look at the bottom number: 10 means tenths and 100 means hundredths. Put the digits in a place-value table and write the decimal point after the ones.

  1. Look at the bottom number. 10 means tenths. Tenths go in the first column after the decimal point.
    2310 is 2 ones and 3 tenths.
  2. Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
    onestenths
    2.32.3
  3. Write the decimal.
    2310 = 2.3

Check. Go back to a fraction: 2.3 = 2310. ✓

Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.

Worked example 6.1.4
Write 0.9 as a fraction.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Count the digits after the point to find the bottom number (10 or 100). Write those digits as the top number. Put any whole number in front.

  1. Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.
    0.9 has 1 digit after the point, so the bottom number is 10.
  2. Read the digits after the point as one number. This is the top number. Ignore any 0 at the front.
    The digits after the point are 9, which is 9.
  3. Write the fraction.
    0.9 = 910   (9 tenths)

Check. Go back: 910 written as a decimal is 0.9. ✓

Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.

Worked example 6.1.5
What number does the arrow show? Write it as a decimal.
12?

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Work out what one gap is worth. Then count on from the left end.

  1. Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.
    The line goes from 1 to 2 in 10 equal gaps.
  2. Work out what one gap is worth. Share the distance between the ends equally.
    1 ÷ 10 = 0.1
  3. Count the gaps from the left end to the point. Count the gaps, not the tick marks.
    The point is 4 gaps after 1.
  4. Work out the number. Start at the left end and add the gaps.
    1 + 4 × 0.1 = 1 + 0.4 = 1.4

Check. Count back from 2: 6 gaps back is 2 − 0.6 = 1.4. ✓

Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.

Worked example 6.1.6
Count on in tenths. Write the missing numbers.
0.6,  0.7,  ?,  0.9,  ?,  1.1

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Find the jump. Then count on in tenths, one jump at a time.

  1. Find the jump between two numbers you know. The numbers go up by the same amount each time.
    0.6 to 0.7: the jump is 0.1 (1 tenth)
  2. Count on in tenths. 10 tenths make 1 whole, so after 0.9 comes 1.0.
    0.6,  0.7,  0.8,  0.9,  1.0,  1.1
  3. Write the missing numbers.
    0.8,  1.0

Check. Count on again from the first number. The jump is always 0.1. ✓

Watch out. Keep one decimal place each time: write 1.0 (not 1) in a tenths sequence.

Worked example 6.1.7
Count back in tenths. Write the missing numbers.
2.2,  2.1,  ?,  1.9,  ?,  1.7

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Find the jump. Then count back in tenths, one jump at a time.

  1. Find the jump between two numbers you know. The numbers go down by the same amount each time.
    2.2 to 2.1: the jump is 0.1 (1 tenth)
  2. Count back in tenths. Going back, 1.0 is the same as 10 tenths, so before 1.0 comes 0.9.
    2.2,  2.1,  2.0,  1.9,  1.8,  1.7
  3. Write the missing numbers.
    2.0,  1.8

Check. Count back again from the first number. The jump is always 0.1. ✓

Watch out. Keep one decimal place each time: write 1.0 (not 1) in a tenths sequence.

Watch out

3/10 is 0.3, not 3.10 and not 0.10. The digit after the point is the number of tenths. Also, do not forget the whole number when you count: after 0.9 comes 1.0, then 1.1.

Exercise 6A  Tenths as decimals

Non-calculator
1
FWhat decimal is shaded in each bar?
(a)
Decimal =
(b)
Decimal =
(c)
Decimal =
2
FQuick-fire! Write each fraction as a decimal.
(a)210 =
(b)510 =
(c)910 =
(d)110 =
(e)710 =
(f)410 =
3
FWrite each decimal as a fraction.
(a)0.3 =
(b)0.7 =
(c)0.1 =
(d)0.9 =
(e)0.6 =
(f)0.4 =
4
FWrite each mixed number as a decimal.
(a)1410 =
(b)3710 =
(c)2110 =
(d)5910 =
5
FWrite each decimal as a mixed number.
(a)1.5 =
(b)3.2 =
(c)4.8 =
(d)2.7 =
6
FThe number line goes from 0 to 1. Write each point as a decimal.
01ABC
(a)A =
(b)B =
(c)C =
7
FCount on in tenths. Write the missing numbers.
(a)0.2,  0.3,  ?,  0.5,  ?,  0.7
(b)0.7,  ?,  0.9,  1.0,  ?,  1.2
(c)1.4,  1.5,  1.6,  ?,  1.8,  ?,  2.0
8
FCount back in tenths. Write the missing numbers.
(a)0.9,  0.8,  ?,  0.6,  ?,  0.4
(b)1.3,  ?,  1.1,  ?,  0.9,  0.8
(c)2.1,  2.0,  ?,  1.8,  1.7,  ?,  1.5
9
FHow many tenths are there in each number?
(a)0.6 = ? tenths
(b)1.3 = ? tenths
(c)2.5 = ? tenths
(d)4.1 = ? tenths
10
PSAisha cuts a 1 m ribbon into 10 equal pieces. She uses 7 of the pieces. What length of ribbon does she use? Give your answer in metres as a decimal.
1 m
11
PSA race is 10 laps long. Tom has run 6 laps.
(a)What decimal of the race has Tom run?
(b)What decimal of the race is left?
12
RWhich is the odd one out?   0.3    310    0.03    three tenths.   Explain.
13
RLeo says, “310 = 3.10.” What mistake has Leo made? Write 310 as a decimal correctly.
14
RI am a decimal between 2 and 3. My tenths digit is double my ones digit. What decimal am I?
6.2

Hundredths and place value

Year 4
Hundredths as fractions and decimals, Place value to two decimal places, Counting in hundredths

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Hundredths and place valueComing soon

Cut each tenth into 10 equal parts. Now the whole is cut into 10 × 10 = 100 equal parts. Each part is one hundredth, written 1/100 or 0.01. So dividing a tenth by 10 makes a hundredth: 0.1 ÷ 10 = 0.01.

1101100one tenth cut into 10 parts
One tenth cut into 10 equal parts. Each part is a hundredth.

A hundred square shows hundredths. Each small square is 0.01. Each row of 10 squares is one tenth, 0.1. If 37 squares are shaded, then 3 rows (3 tenths) and 7 more squares (7 hundredths) are shaded. That is 37/100 = 0.37.

37 small squares shaded: 37/100 = 0.37. That is 3 tenths and 7 hundredths.

Two decimal places. The second digit after the point is the hundredths digit. In 0.37 there are 0 ones, 3 tenths and 7 hundredths.

Ones10tenths0.1.1.1.13hundredths0.01.01.01.01.01.01.01.017
0.37 = 0 ones, 3 tenths and 7 hundredths.

A zero keeps a place. 0.05 is not the same as 0.5. In 0.05 there are no tenths, so the tenths column holds a 0. Look at the squares.


0.05 (5 hundredths)

0.5 (5 tenths)
0.05 is a lot smaller than 0.5.

The value of each digit. In 3.45 the 3 is worth 3 ones (3), the 4 is worth 4 tenths (0.4) and the 5 is worth 5 hundredths (0.05). We can split a number up like this: 3.45 = 3 + 0.4 + 0.05.

Ones11113tenths0.1.1.1.1.14hundredths0.01.01.01.01.01.015
3.45 = 3 + 0.4 + 0.05.

On a number line. Zoom in on the line from 0.3 to 0.4. It is cut into 10 gaps. Each gap is a hundredth, 0.01.

0.300.310.320.330.340.350.360.370.380.390.40A
A is 7 gaps after 0.3, so A = 0.37.

Counting in hundredths. 0.07, 0.08, 0.09, then 0.10 (that is 10 hundredths = 1 tenth), 0.11, 0.12. And past a whole: 0.98, 0.99, 1.00, 1.01. Counting back: 0.12, 0.11, 0.10, 0.09.

Key words. A hundredth is one of 100 equal parts of a whole. It is the second column after the decimal point.

Key ideas

  • A hundredth is 1 of 100 equal parts: 1/100 = 0.01.
  • 10 hundredths make 1 tenth: 0.10 = 0.1.
  • The first digit after the point is tenths and the second digit is hundredths.
  • 37 hundredths = 37/100 = 0.37 = 3 tenths and 7 hundredths.
  • Use a 0 to hold a place: 5 hundredths is 0.05 (not 0.5).
  • Split a decimal by the value of its digits: 3.45 = 3 + 0.4 + 0.05.
Worked example 6.2.1
What decimal is shaded?

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. A hundred square has 100 small squares. Each is one hundredth. Count the shaded squares, then write the decimal.

  1. Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.
    10 × 10 = 100 squares
  2. Count the shaded squares. Count the full rows first (10 squares each), then the extra squares.
    3 full rows = 30 squares
    30 + 7 = 37 squares
  3. Write the fraction. The top number is the shaded squares.
    37100
  4. Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.
    onestenthshundredths
    0.370.37

    37 hundredths = 0 ones, 3 tenths and 7 hundredths, so 0.37

Check. Go back: 0.37 is 37100. ✓

Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.

Worked example 6.2.2
Write 7/100 as a decimal.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Look at the bottom number: 10 means tenths and 100 means hundredths. Put the digits in a place-value table and write the decimal point after the ones.

  1. Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
    7100 is 7 hundredths.
  2. Notice there are no tenths. 7 hundredths is less than 1 tenth (1 tenth = 10 hundredths). The tenths column must hold a 0.
    0 tenths and 7 hundredths
  3. Look at the picture.
  4. Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
    onestenthshundredths
    0.070.07
  5. Write the decimal.
    7100 = 0.07

Check. Go back to a fraction: 0.07 = 7100. ✓

Watch out. 7 hundredths is 0.07, not 0.7. The 0 in the tenths column keeps the 7 in the hundredths column.

Worked example 6.2.3
Write 0.63 as a fraction.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Count the digits after the point to find the bottom number (10 or 100). Write those digits as the top number. Put any whole number in front.

  1. Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.
    0.63 has 2 digits after the point, so the bottom number is 100.
  2. Read the digits after the point as one number. This is the top number. Ignore any 0 at the front.
    The digits after the point are 63, which is 63.
  3. Write the fraction.
    0.63 = 63100   (63 hundredths)

Check. Go back: 63100 written as a decimal is 0.63. ✓

Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.

Worked example 6.2.4
Write the number that has 8 ones, 0 tenths and 4 hundredths.

Key words. Place value means that a digit is worth different amounts in different columns. After the decimal point the columns are tenths (0.1) and hundredths (0.01).

Method. Put each digit in its column of the place-value table. Write a 0 in any empty column. Then write the number with the point after the ones.

  1. Draw a place-value table. The columns are ones, then tenths, then hundredths.
    onestenthshundredths
    8.048.04
  2. Write each digit in its column. A column with none in it still needs a 0 so the other digits stay in the right place.
    8 ones, 0 tenths and 4 hundredths
  3. Write the number. Put the decimal point between the ones and the tenths.
    8.04

Check. Read it back: 8.04 is 8 ones, 0 tenths and 4 hundredths. ✓

Watch out. Do not leave out a 0. Two ones, no tenths and 7 hundredths is 2.07, not 2.7.

Worked example 6.2.5
Split 5.82 into the value of each digit.

Key words. Place value means that a digit is worth different amounts in different columns. After the decimal point the columns are tenths (0.1) and hundredths (0.01).

Method. Split the number into the value of each digit and write them as an addition.

  1. Write the number in a place-value table.
    onestenthshundredths
    5.825.82
  2. Work out the value of each digit. A zero digit is worth nothing, so we can leave it out.
    5 ones = 5
    8 tenths = 0.8
    2 hundredths = 0.02
  3. Write the parts as an addition.
    5.82 = 5 + 0.8 + 0.02

Check. Add the parts: 5 + 0.8 + 0.02 = 5.82. ✓

Watch out. Write 0.4 for 4 tenths, not 4. Write 0.05 for 5 hundredths, not 0.5.

Worked example 6.2.6
Count on in hundredths. Write the missing numbers.
0.06,  0.07,  ?,  0.09,  ?,  ?,  0.12

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Find the jump. Then count on in hundredths, one jump at a time.

  1. Find the jump between two numbers you know. The numbers go up by the same amount each time.
    0.06 to 0.07: the jump is 0.01 (1 hundredth)
  2. Count on in hundredths. 10 hundredths make 1 tenth, so after 0.09 comes 0.10. And 100 hundredths make 1 whole, so after 0.99 comes 1.00.
    0.06,  0.07,  0.08,  0.09,  0.10,  0.11,  0.12
  3. Write the missing numbers.
    0.08,  0.10,  0.11

Check. Count on again from the first number. The jump is always 0.01. ✓

Watch out. Keep two decimal places each time: write 0.10 (not 0.1) and 1.00 (not 1) in a hundredths sequence.

Worked example 6.2.7
What number does the arrow show?
0.300.40?

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Work out what one gap is worth. Then count on from the left end.

  1. Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.
    The line goes from 0.3 to 0.4 in 10 equal gaps.
  2. Work out what one gap is worth. Share the distance between the ends equally.
    0.1 ÷ 10 = 0.01
  3. Count the gaps from the left end to the point. Count the gaps, not the tick marks.
    The point is 7 gaps after 0.3.
  4. Work out the number. Start at the left end and add the gaps.
    0.3 + 7 × 0.01 = 0.3 + 0.07 = 0.37

Check. Count back from 0.4: 3 gaps back is 0.4 − 0.03 = 0.37. ✓

Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.

Watch out

Do not drop the zero. 7 hundredths is 0.07. If you write 0.7 you have written 7 tenths, which is ten times bigger. Also: after 0.09 comes 0.10 (10 hundredths), not 0.010.

Exercise 6B  Hundredths and place value

Non-calculator
1
FWhat decimal is shaded in each hundred square?
(a)
Decimal =
(b)
Decimal =
(c)
Decimal =
2
FQuick-fire! Write each fraction as a decimal.
(a)9100 =
(b)45100 =
(c)70100 =
(d)3100 =
(e)99100 =
(f)12100 =
3
FWrite each decimal as a fraction.
(a)0.21 =
(b)0.08 =
(c)0.60 =
(d)0.99 =
(e)0.35 =
(f)0.04 =
4
FWrite the number shown in each place-value chart.
(a)
Ones1tenths0.1.1.1.1hundredths0.01.01.01.01.01
Number =
(b)
Ones11tenths0.1.1.1.1.1.1hundredths0.01.01.01
Number =
(c)
Ones111tenths0.1hundredths0.01.01.01.01.01.01.01.01
Number =
5
FWrite each number as a decimal.
(a)4 ones, 2 tenths and 6 hundredths =
(b)0 ones, 0 tenths and 9 hundredths =
(c)7 ones, 0 tenths and 5 hundredths =
(d)2 ones, 9 tenths and 1 hundredth =
(e)0 ones, 6 tenths and 0 hundredths =
6
FWhat is the value of the underlined digit? Write the digit and its value.
(a)3.47
(b)5.82
(c)0.91
(d)6.05
(e)7.28
(f)12.34
7
FWrite the digit in the column asked for.
(a)The tenths digit of 6.72 is
(b)The hundredths digit of 0.58 is
(c)The tenths digit of 9.04 is
(d)The hundredths digit of 3.19 is
8
FSplit each number into the value of its digits. For example, 2.31 = 2 + 0.3 + 0.01.
(a)3.45 =
(b)6.08 =
(c)0.72 =
9
FCount in hundredths. Write the missing numbers.
(a)0.04,  0.05,  ?,  0.07,  0.08,  ?
(b)0.97,  0.98,  ?,  1.00,  ?,  1.02
(c)0.13,  0.12,  ?,  0.10,  ?,  0.08
10
FThe number line goes from 0.5 to 0.6. Write each point as a decimal.
0.500.60ABC
(a)A =
(b)B =
(c)C =
11
FHow many hundredths are there in each number?
(a)0.3 = ? hundredths
(b)0.8 = ? hundredths
(c)1.5 = ? hundredths
(d)2.04 = ? hundredths
12
PS1 cm is one hundredth of a metre. Write each length in metres as a decimal.
(a)17 cm =
(b)4 cm =
(c)85 cm =
13
RMia says, “0.5 and 0.05 are the same number.” Is she right? Use a hundred square to explain.
14
RI am a number between 0.3 and 0.4. My hundredths digit is double my tenths digit. What number am I?
6.3

Halves, quarters and three quarters

Year 4
Decimal equivalents of 1/2, 1/4 and 3/4, Simple measures with decimals

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Halves, quarters and three quartersComing soon

Some fractions are used so often that it is worth knowing them as decimals. Use a hundred square. It has 100 small squares, and each one is 0.01.


1/4 = 0.25

1/2 = 0.5

3/4 = 0.75
A quarter, a half and three quarters of a hundred square.

Why is a half 0.5 and also 0.50? A half is 5 tenths, 0.5. It is also 50 hundredths, 0.50. A 0 on the end of a decimal does not change the number, so 0.5 = 0.50.

00.250.500.751ABC
On the number line from 0 to 1: A = 1/4 = 0.25, B = 1/2 = 0.5 and C = 3/4 = 0.75.

Going the other way. To write 0.75 as a fraction, write it as hundredths: 75/100. Then divide the top and the bottom by 25: 75 ÷ 25 = 3 and 100 ÷ 25 = 4. So 0.75 = 3/4.

Money. There are 100p in £1. So a half of £1 is 50p = £0.50, a quarter of £1 is 25p = £0.25, and three quarters of £1 is 75p = £0.75.

50p20p5p
50p + 20p + 5p = 75p = £0.75, which is three quarters of £1.

Measures. We use these decimals for lengths, masses and capacities. 2.5 m is 2 and a half metres. 1.75 kg is 1 and three quarters of a kilogram. 0.25 litres is a quarter of a litre.

11.251.501.752A
A parcel has a mass of 1.75 kg. That is 1 and 3/4 kg.

Key words. A hundred square has 100 small squares. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Key ideas

  • 1/2 = 0.5 (also 0.50 and 5/10).
  • 1/4 = 0.25 (25 hundredths).
  • 3/4 = 0.75 (75 hundredths).
  • A half of £1 is 50p = £0.50. A quarter is 25p. Three quarters is 75p.
  • With a whole number: 2 1/2 = 2.5, 3 3/4 = 3.75.
  • A decimal like 0.5 does not change if you add a 0 on the end: 0.5 = 0.50.
Worked example 6.3.1
Write 1/4 as a decimal.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

  1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
    100 ÷ 4 = 25 squares in each part
  2. Find how many squares are in 14. 1 part of 25 squares.
    1 part = 25 squares
  3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
    14 = 25100
  4. Write it as a decimal. 25 hundredths is 0 ones, 2 tenths and 5 hundredths.
    25100 = 0.25

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Worked example 6.3.2
Write 3/4 as a decimal.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

  1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
    100 ÷ 4 = 25 squares in each part
  2. Find how many squares are in 34. 3 parts of 25 squares.
    3 × 25 = 75 squares
  3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
    34 = 75100
  4. Write it as a decimal. 75 hundredths is 0 ones, 7 tenths and 5 hundredths.
    75100 = 0.75

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Worked example 6.3.3
Write 0.75 as a fraction in its simplest form.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

  1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
    75 hundredths = 75100
  2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
    75 and 100 both divide by 25.
  3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
    75 ÷ 25 = 3 and 100 ÷ 25 = 4
    75100 = 34
  4. Write the fraction.
    0.75 = 34

Check. Go back to a decimal: 34 of 100 is 75, which is 75 hundredths = 0.75. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Worked example 6.3.4
Write 0.5 as a fraction in its simplest form.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

  1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
    50 hundredths = 50100
  2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
    50 and 100 both divide by 50.
  3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
    50 ÷ 50 = 1 and 100 ÷ 50 = 2
    50100 = 12
  4. Write the fraction.
    0.5 = 12

Check. Go back to a decimal: 12 of 100 is 50, which is 50 hundredths = 0.50. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Worked example 6.3.5
Write 2 1/4 as a decimal.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

  1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
    100 ÷ 4 = 25 squares in each part
  2. Find how many squares are in 14. 1 part of 25 squares.
    1 part = 25 squares
  3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
    14 = 25100
  4. Write it as a decimal. 25 hundredths is 0 ones, 2 tenths and 5 hundredths.
    25100 = 0.25
  5. Add the whole number. The whole number goes in front of the point.
    2 + 0.25 = 2.25

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Worked example 6.3.6
A parcel has a mass of 1.75 kg. Write 1.75 as a mixed number.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

  1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
    75 hundredths = 75100
  2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
    75 and 100 both divide by 25.
  3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
    75 ÷ 25 = 3 and 100 ÷ 25 = 4
    75100 = 34
  4. Put the whole number in front.
    1 and 34 = 134
  5. Write the fraction.
    1.75 = 134

Check. Go back to a decimal: 34 of 100 is 75, which is 75 hundredths = 0.75. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Worked example 6.3.7
Work out 3/4 of £2. Give your answer in pounds.

Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.

Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.

  1. Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.
    £2 = 2 × 100 = 200p
  2. Find one part: divide by the bottom number, 4. The bottom number says how many equal parts.
    200p ÷ 4 = 50p
  3. Multiply by the top number, 3. The top number says how many parts we take.
    50p × 3 = 150p
  4. Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.
    150p = £1.50

Check. 50p × 4 = 200p, so 4 parts make the whole amount. ✓

Watch out. Write money with two decimal places: £3.50, not £3.5.

Watch out

1/4 is 0.25, not 0.4 or 0.14. A quarter is 25 hundredths. And 0.5 is not the same as 0.05: 0.5 is a half but 0.05 is only 5 hundredths. Do not forget: 3/4 is 0.75, so it is MORE than a half.

Exercise 6C  Halves, quarters and three quarters

Non-calculator
1
FThe hundred squares are shaded. Write the decimal that is shaded.
(a)
Decimal =
(b)
Decimal =
(c)
Decimal =
2
FQuick-fire! Write each fraction as a decimal.
(a)12 =
(b)34 =
(c)14 =
(d)24 =
(e)510 =
(f)25100 =
3
FWrite each decimal as a fraction. Give each answer in its simplest form.
(a)0.5 =
(b)0.25 =
(c)0.75 =
(d)0.1 =
(e)0.01 =
(f)0.50 =
4
FWrite each mixed number as a decimal.
(a)212 =
(b)334 =
(c)114 =
(d)612 =
5
FWrite each decimal as a mixed number.
(a)2.5 =
(b)4.75 =
(c)1.25 =
(d)7.5 =
(e)3.25 =
6
FThe number line goes from 0 to 1. Write each point as a decimal.
01ABC
(a)A =
(b)B =
(c)C =
7
FWrite each measure as a decimal.
(a)12 m =
(b)34 kg =
(c)114 litres =
(d)212 km =
8
FWork out each fraction of the money. Give your answers in pounds.
(a)12 of £1 =
(b)14 of £2 =
(c)34 of £4 =
(d)12 of £5 =
9
PSPriya pours 1 litre of juice into 4 equal glasses.
1 litre
(a)What fraction of a litre is in each glass? Write it as a decimal.
(b)She drinks 3 of the glasses. What decimal of a litre is that?
10
PSA rope is 2 3/4 m long. Zara cuts off 1 m.
(a)Write the length of the rope as a decimal.
(b)How long is the rope now? Give your answer as a decimal.
11
RTom says, “14 = 0.4, because there is a 4 on the bottom.” Is Tom right? Explain.
12
RMatch each fraction to its decimal.   A 12   B 34   C 14   D 110
Decimals:   0.1    0.25    0.5    0.75
13
RWhich is the odd one out?   0.5    510    12    0.05.   Explain.
14
RI am a fraction with 4 on the bottom. I am more than 0.5 and less than 1. What fraction am I? Write me as a decimal too.
6.4

Dividing by 10 and 100

Year 4
Divide 1- and 2-digit numbers by 10 and 100, Value of digits as ones, tenths and hundredths

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Dividing by 10 and 100Coming soon

When you divide by 10, the number gets 10 times smaller. Every digit moves one column to the right. When you divide by 100, every digit moves two columns to the right. The digits are the ones that move. The decimal point stays where it is.

TensOnestenthshundredthsStart÷ 105353
53 ÷ 10 = 5.3. The 5 moves from the tens column to the ones column and the 3 moves from the ones column to the tenths column.

Dividing by 100. Move the digits two columns.

TensOnestenthshundredthsStart÷ 10053053
53 ÷ 100 = 0.53. Each digit moves two columns to the right. The empty ones column gets a 0.

Fill the gaps with zeros. 7 ÷ 10 = 0.7 and 7 ÷ 100 = 0.07. In 0.07 there are 0 ones and 0 tenths, so both columns need a 0.

TensOnestenthshundredthsStart÷ 1007007
7 ÷ 100 = 0.07. The 7 moves two columns, to the hundredths column.

Tidying up. 40 ÷ 10 = 4.0, and 4.0 is just 4. And 30 ÷ 100 = 0.30, which is 0.3. The last 0 is not needed.

Why? Dividing by 100 is the same as dividing by 10 twice. 53 ÷ 10 = 5.3 and then 5.3 ÷ 10 = 0.53. The opposite is multiplying: 0.53 × 100 = 53. The digits move left.

Measures. There are 100 cm in 1 m. To change cm to m, divide by 100: 250 cm ÷ 100 = 2.5 m. There are 10 mm in 1 cm, so to change mm to cm, divide by 10: 36 mm ÷ 10 = 3.6 cm. Money. There are 100p in £1, so 450p ÷ 100 = £4.50.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move to the right.

Key ideas

  • ÷ 10: every digit moves 1 column to the right.
  • ÷ 100: every digit moves 2 columns to the right.
  • Put a 0 in any empty column: 7 ÷ 100 = 0.07.
  • Dividing by 100 is the same as dividing by 10 twice.
  • The opposite of dividing is multiplying: the digits move left.
  • cm ÷ 100 = m, mm ÷ 10 = cm, p ÷ 100 = £.
Worked example 6.4.1
Work out 6 ÷ 10.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 10 moves each digit 1 place to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 10 makes every digit 10 times smaller.
    TensOnestenthshundredthsStart÷ 106
  2. Move every digit 1 column to the right. Each digit slides one column to the right, to a column that is worth 10 times less.
    TensOnestenthshundredthsStart÷ 10606
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones.
    6 ÷ 10 = 0.6

Check. Go the other way: 0.6 × 10 = 6. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.2
Work out 48 ÷ 10.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 10 moves each digit 1 place to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 10 makes every digit 10 times smaller.
    TensOnestenthshundredthsStart÷ 1048
  2. Move every digit 1 column to the right. Each digit slides one column to the right, to a column that is worth 10 times less.
    TensOnestenthshundredthsStart÷ 104848
  3. Write the answer. Put the decimal point after the ones.
    48 ÷ 10 = 4.8

Check. Go the other way: 4.8 × 10 = 48. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.3
Work out 48 ÷ 100.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 100 moves each digit 2 places to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 100 makes every digit 100 times smaller.
    TensOnestenthshundredthsStart÷ 10048
  2. Move every digit 2 columns to the right. Each digit slides two columns to the right, because dividing by 100 is dividing by 10 twice.
    TensOnestenthshundredthsStart÷ 10048048
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones.
    48 ÷ 100 = 0.48

Check. Go the other way: 0.48 × 100 = 48. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.4
Work out 7 ÷ 100.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 100 moves each digit 2 places to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 100 makes every digit 100 times smaller.
    TensOnestenthshundredthsStart÷ 1007
  2. Move every digit 2 columns to the right. Each digit slides two columns to the right, because dividing by 100 is dividing by 10 twice.
    TensOnestenthshundredthsStart÷ 1007007
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones.
    7 ÷ 100 = 0.07

Check. Go the other way: 0.07 × 100 = 7. ✓

Watch out. The digits move, not the decimal point. And 5 ÷ 100 is 0.05: you need a 0 in the tenths column as well as the ones column.

Worked example 6.4.5
Work out 30 ÷ 100.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 100 moves each digit 2 places to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 100 makes every digit 100 times smaller.
    TensOnestenthshundredthsStart÷ 10030
  2. Move every digit 2 columns to the right. Each digit slides two columns to the right, because dividing by 100 is dividing by 10 twice.
    TensOnestenthshundredthsStart÷ 10030030
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones. The last 0 is not needed: 4.0 is the same as 4, and 0.30 is the same as 0.3.
    30 ÷ 100 = 0.3

Check. Go the other way: 0.3 × 100 = 30. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.6
Find the missing number.   ? ÷ 10 = 3.6

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Use the opposite operation. The opposite of dividing is multiplying.

  1. Think about the opposite operation. The opposite of dividing by 10 is multiplying by 10.
    ? = 3.6 × 10
  2. Move every digit 1 column to the left. Multiplying makes each digit bigger, so the digits move left.
    3.6 × 10 = 36
  3. Write the answer.
    36 ÷ 10 = 3.6

Check. Check: 36 ÷ 10 = 3.6. ✓

Watch out. Dividing moves digits right. To undo it, move them left.

Worked example 6.4.7
Find the missing number.   52 ÷ ? = 0.52

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Count how many columns the digits moved to the right. One column is ÷ 10 and two columns is ÷ 100.

  1. Compare the two numbers. 52 became 0.52.
    52 → 0.52
  2. Count how many columns the digits moved. Each digit moved to the right.
    The digits moved 2 columns to the right.
  3. Decide what we divided by. 1 column means ÷ 10. 2 columns means ÷ 100.
    100

Check. Check: 52 ÷ 100 = 0.52. ✓

Watch out. Compare where the digits are, not how long the number looks.

Worked example 6.4.8
Change 340 cm into metres.

Key words. Convert means change from one unit to another. 1 m = 100 cm. 1 cm = 10 mm.

Method. There are 100 cm in 1 m. Divide by 100 to change cm into m.

  1. Find how many of the small unit make one of the big unit. We need this to change units.
    1 m = 100 cm
  2. Choose the operation. We are changing cm into m. A m is bigger, so we need fewer of them: divide by 100.
    340 ÷ 100
  3. Move the digits 2 columns to the right. Dividing by 100 makes each digit 100 times smaller.
    340 ÷ 100 = 3.4
  4. Write the answer with the unit.
    340 cm = 3.4 m

Check. Go back: 3.4 × 100 = 340. ✓

Watch out. Fewer m than cm: the number should get smaller. If it does not, you used the wrong operation.

Watch out

The digits move. You do not just add a point. 7 ÷ 100 is 0.07, not 0.7 and not 7.00. Also, dividing makes the number SMALLER, so the digits must move to the right. If the answer is bigger than what you started with, something has gone wrong.

Exercise 6D  Dividing by 10 and 100

Non-calculator
1
FQuick-fire! Divide each number by 10.
(a)3 ÷ 10 =
(b)9 ÷ 10 =
(c)20 ÷ 10 =
(d)45 ÷ 10 =
(e)70 ÷ 10 =
(f)86 ÷ 10 =
2
FQuick-fire! Divide each number by 100.
(a)4 ÷ 100 =
(b)8 ÷ 100 =
(c)60 ÷ 100 =
(d)37 ÷ 100 =
(e)90 ÷ 100 =
(f)52 ÷ 100 =
3
FUse the place-value charts. Write the answers.
(a)
TensOnestenthshundredthsStart÷ 105
5 ÷ 10 =
(b)
TensOnestenthshundredthsStart÷ 1034
34 ÷ 10 =
(c)
TensOnestenthshundredthsStart÷ 1007
7 ÷ 100 =
(d)
TensOnestenthshundredthsStart÷ 10026
26 ÷ 100 =
4
FFind each missing number.
(a)? ÷ 10 = 7
(b)? ÷ 100 = 0.9
(c)? ÷ 10 = 4.2
(d)? ÷ 100 = 0.35
5
FIs the missing number 10 or 100?
(a)8 ÷ ? = 0.8
(b)63 ÷ ? = 0.63
(c)95 ÷ ? = 9.5
(d)4 ÷ ? = 0.04
6
FEach number is divided by 10 to make the next one. Write the missing numbers.
(a)600,  60,  ?,  0.6,  ?
(b)90,  9,  ?,  ?
(c)70,  ?,  0.7,  ?
7
FChange each length into the bigger unit.
(a)300 cm = ? m
(b)450 cm = ? m
(c)36 mm = ? cm
(d)7 mm = ? cm
8
FThis time change metres into centimetres. Multiply by 100.
(a)3.5 m = ? cm
(b)0.72 m = ? cm
(c)6 m = ? cm
9
PSA rope is 6 m long.
??????????6 m
(a)The rope is cut into 10 equal pieces. How long is each piece?
(b)Another 6 m rope is cut into 100 equal pieces. How long is each piece?
10
PSWrite each stride length in metres.
(a)Tom’s stride is 75 cm long.
(b)Amira’s stride is 68 cm long.
11
RJack says, “5 ÷ 10 = 0.05.” What mistake has Jack made? What is the correct answer?
12
RAlways, sometimes or never?   When you divide a two-digit number by 100, the answer is less than 1.
13
RWhich two calculations have the answer 0.4? Tick two boxes.
A 4 ÷ 10    B 40 ÷ 100    C 40 ÷ 10    D 4 ÷ 100    E 400 ÷ 100
14
RAmira divides a number by 10 and then divides her answer by 10 again. What single number could she have divided by instead? Show it with 50.
6.5

Comparing, ordering and rounding decimals

Year 4
Compare numbers with the same number of decimal places, Order decimals, Round to the nearest whole number

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Comparing, ordering and rounding decimalsComing soon

To compare two decimals, write them in a place-value table with the decimal points lined up. Then compare the digits from the left. The first column where the digits are different tells you which number is bigger.

onestenthshundredths
5.345.34
5.395.39
onestenths
4.84.8
4.34.3
Left: 5.34 and 5.39 have the same ones and tenths, but 4 hundredths is less than 9 hundredths, so 5.34 < 5.39. Right: 8 tenths > 3 tenths, so 4.8 > 4.3.

A picture helps. Look at 0.45 and 0.54. The first has 4 full rows and 5 squares. The second has 5 full rows and 4 squares. 5 tenths is more than 4 tenths, so 0.54 is bigger.


0.45

0.54
0.45 < 0.54.

Ordering means putting numbers in a list. Compare the ones, then the tenths, then the hundredths. For example, to order 0.82, 0.28, 0.88 and 0.08 from smallest to biggest: all have 0 ones. The tenths digits are 8, 2, 8 and 0. So 0.08 is the smallest, then 0.28. The other two both have 8 tenths, so compare hundredths: 0.82 < 0.88. The order is 0.08, 0.28, 0.82, 0.88.

Rounding to the nearest whole number. Look at 3.4. It is between 3 and 4. On a number line, 3.4 is closer to 3.

33.54
3.4 is between 3 and 4. It is closer to 3, so 3.4 rounds to 3.

The halfway point between 3 and 4 is 3.5. Numbers below 3.5 are closer to 3. Numbers from 3.5 up are closer to 4 (halfway, 3.5, rounds up).

33.54
3.7 is closer to 4, so 3.7 rounds to 4.

The quick rule: look at the tenths digit (the first digit after the point). If it is 5 or more, round up to the next whole number. If it is 4 or less, round down (keep the whole number).

Key words. To compare is to say which is bigger. To order is to put in a list. To round is to change to a nearby number that is easier to use.

Key ideas

  • Line up the decimal points and compare the digits from the left.
  • The first column where the digits are different decides which number is bigger.
  • Order: compare ones, then tenths, then hundredths. List all the numbers.
  • Rounding to the nearest whole number: look at the tenths digit.
  • 5 or more: round up. 4 or less: round down.
  • Halfway (like 3.5) rounds up.
Worked example 6.5.1
Write < or > in the box.   4.8  [ ]   4.3

Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.

Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.

  1. Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
    onestenths
    4.84.8
    4.34.3
  2. Compare the digits from the left. The first column where the digits are different decides.
    ones: 4 and 4 are the same, so look at the next column.
    tenths: 8 and 3 are different. 8 > 3, so 4.8 is bigger.
  3. Write the answer. < means “is less than” and > means “is greater than”.
    4.8 > 4.3

Check. Picture a number line: 4.3 is to the left of 4.8. ✓

Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.

Worked example 6.5.2
Write < or > in the box.   5.34  [ ]   5.39

Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.

Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.

  1. Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
    onestenthshundredths
    5.345.34
    5.395.39
  2. Compare the digits from the left. The first column where the digits are different decides.
    ones: 5 and 5 are the same, so look at the next column.
    tenths: 3 and 3 are the same, so look at the next column.
    hundredths: 4 and 9 are different. 4 < 9, so 5.34 is smaller.
  3. Write the answer. < means “is less than” and > means “is greater than”.
    5.34 < 5.39

Check. Picture a number line: 5.34 is to the left of 5.39. ✓

Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.

Worked example 6.5.3
Write < or > in the box.   2.45  [ ]   3.12

Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.

Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.

  1. Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
    onestenthshundredths
    2.452.45
    3.123.12
  2. Compare the digits from the left. The first column where the digits are different decides.
    ones: 2 and 3 are different. 2 < 3, so 2.45 is smaller.
  3. Write the answer. < means “is less than” and > means “is greater than”.
    2.45 < 3.12

Check. Picture a number line: 2.45 is to the left of 3.12. ✓

Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.

Worked example 6.5.4
Write these numbers in order, smallest first.   0.82,   0.28,   0.88,   0.08

Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.

Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.

  1. Write the numbers in a place-value table. Line up the decimal points.
    onestenthshundredths
    0.820.82
    0.280.28
    0.880.88
    0.080.08
  2. Compare the columns from the left. Where the digits are the same, look at the next column to the right.
    Ones: 0.82 has 0, 0.28 has 0, 0.88 has 0, 0.08 has 0. All the same, so look at the next column.
    Tenths: 0.82 has 8, 0.28 has 2, 0.88 has 8, 0.08 has 0. Smallest to biggest: 0, 2, 8.
    Hundredths: 0.82 has 2, 0.88 has 8. Smallest to biggest: 2, 8.
  3. Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.
    0.08,  0.28,  0.82,  0.88

Check. Count them: 4 numbers in the question and 4 in the answer. ✓

Watch out. Do not forget a number. Tick each one off as you write it.

Worked example 6.5.5
Write these numbers in order, biggest first.   3.6,   3.1,   2.9,   3.0

Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.

Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them biggest first.

  1. Write the numbers in a place-value table. Line up the decimal points.
    onestenths
    3.63.6
    3.13.1
    2.92.9
    3.03.0
  2. Compare the columns from the left. Where the digits are the same, look at the next column to the right.
    Ones: 3.6 has 3, 3.1 has 3, 2.9 has 2, 3.0 has 3. Smallest to biggest: 2, 3.
    Tenths: 3.6 has 6, 3.1 has 1, 3.0 has 0. Smallest to biggest: 0, 1, 6.
  3. Write them biggest first. Write the ORIGINAL numbers and check that you have used every one.
    3.6,  3.1,  3.0,  2.9

Check. Count them: 4 numbers in the question and 4 in the answer. ✓

Watch out. Do not forget a number. Tick each one off as you write it.

Worked example 6.5.6
Round 4.3 to the nearest whole number.

Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.

Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.

  1. Find the two whole numbers that 4.3 is between. Rounding to the nearest whole number means choosing the closest whole number.
    4  <  4.3  <  5
  2. Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.
    The tenths digit is 3.
  3. Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)
    3 is 4 or less, so round down.
  4. Look at the number line. The orange dot is 4.3. The green ring is the nearest whole number.
    44.55
  5. Write the answer.
    4.3 ≈ 4 (to the nearest whole number)

Check. Distances: 4.3 − 4 = 0.3 and 5 − 4.3 = 0.7. 4 is the nearer whole number. ✓

Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.

Worked example 6.5.7
Round 7.6 to the nearest whole number.

Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.

Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.

  1. Find the two whole numbers that 7.6 is between. Rounding to the nearest whole number means choosing the closest whole number.
    7  <  7.6  <  8
  2. Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.
    The tenths digit is 6.
  3. Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)
    6 is 5 or more, so round up.
  4. Look at the number line. The orange dot is 7.6. The green ring is the nearest whole number.
    77.58
  5. Write the answer.
    7.6 ≈ 8 (to the nearest whole number)

Check. Distances: 7.6 − 7 = 0.6 and 8 − 7.6 = 0.4. 8 is the nearer whole number. ✓

Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.

Worked example 6.5.8
Round 5.5 to the nearest whole number.

Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.

Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.

  1. Find the two whole numbers that 5.5 is between. Rounding to the nearest whole number means choosing the closest whole number.
    5  <  5.5  <  6
  2. Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.
    The tenths digit is 5.
  3. Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)
    5 is 5 or more, so round up.
  4. Look at the number line. The orange dot is 5.5. The green ring is the nearest whole number.
    55.56
  5. Write the answer.
    5.5 ≈ 6 (to the nearest whole number)

Check. Distances: 5.5 − 5 = 0.5 and 6 − 5.5 = 0.5. 6 is the one we choose when exactly halfway. ✓

Watch out. Exactly halfway (like 6.5) always rounds UP.

Watch out

More digits does not mean a bigger number. 0.45 is smaller than 0.5 even though 45 is bigger than 5. Write 0.5 as 0.50 and compare 45 hundredths with 50 hundredths. And when you round, only look at the tenths digit: 4.49 would round down because the tenths digit is 4.

Exercise 6E  Comparing, ordering and rounding decimals

Non-calculator
1
FLook at the hundred squares. Write < or > between the numbers.
(a)

0.4

0.7
0.4  [ ]   0.7
(b)

0.35

0.53
0.35  [ ]   0.53
(c)

0.8

0.08
0.8  [ ]   0.08
2
FQuick-fire! Write <, > or = in each box.
(a)0.3  [ ]   0.8
(b)2.5  [ ]   2.1
(c)4.0  [ ]   3.9
(d)6.7  [ ]   6.9
(e)9.1  [ ]   8.9
(f)3.3  [ ]   3.3
3
FQuick-fire! Write <, > or = in each box.
(a)0.34  [ ]   0.43
(b)5.62  [ ]   5.26
(c)1.07  [ ]   1.70
(d)3.45  [ ]   3.45
(e)0.58  [ ]   0.59
(f)7.91  [ ]   7.19
4
FWrite each set of numbers in order, smallest first.
(a)0.6,  0.2,  0.9,  0.4
(b)3.7,  3.1,  2.8,  3.0
(c)0.45,  0.54,  0.04,  0.40
5
FWrite each set of numbers in order, biggest first.
(a)1.5,  5.1,  1.1,  5.5
(b)0.72,  0.27,  0.77,  0.07
6
FThe number line goes from 5 to 6. Write each point as a decimal. Then write the three numbers in order, smallest first.
56ABC
(a)A =
(b)B =
(c)C =
(d)Smallest first:
7
FRound each number to the nearest whole number.
(a)3.4 ≈
(b)6.5 ≈
(c)8.9 ≈
(d)12.1 ≈
(e)0.7 ≈
(f)19.5 ≈
8
FRound each number to the nearest whole number. The number lines will help you.
(a)
23
2.3 ≈
(b)
67
6.8 ≈
(c)
910
9.5 ≈
9
FBetween which two whole numbers does each number lie? Which one is it closer to?
(a)6.2 is between ? and ?
(b)14.8 is between ? and ?
(c)0.4 is between ? and ?
10
PSThree children jump in a long jump competition. Amira jumps 2.35 m, Noah jumps 2.53 m and Tom jumps 2.30 m.
(a)Write the jumps in order, longest first.
(b)Write the jumps in order, shortest first.
11
PSRound each measure to the nearest whole number.
(a)A walk is 3.6 km long. Round the length to the nearest whole number of km.
(b)A jug holds 7.2 litres. Round the amount to the nearest whole number of litres.
(c)A parcel has a mass of 12.5 kg. Round the mass to the nearest whole number of kg.
12
RSam says, “0.45 is bigger than 0.5, because 45 is bigger than 5.” Is Sam right? Explain.
13
RWhich two numbers round to 5 when rounded to the nearest whole number? Tick two boxes.
A 4.5    B 4.4    C 5.4    D 5.5
14
RA number with one decimal place is rounded to the nearest whole number and the answer is 8. What is the smallest the number could be? What is the biggest?
6.6

Money: pounds and pence

Year 4
Pounds and pence, Writing, converting and comparing money, Estimate and compare money

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Money: pounds and penceComing soon

In the UK we use pounds (£) and pence (p). 100 pence make 1 pound. These are the coins: 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2.

1p2p5p10p20p50p£1£2
The coins. The 20p and 50p coins have 7 sides.

And these are the notes: £5, £10, £20 and £50.

£5£10£20£50
The notes.

Writing money. Money is a decimal. The pounds go before the decimal point and the pence go after it, with two digits. Three pounds and five pence is £3.05, not £3.5 (that would be £3.50). Forty-five pence can be written as 45p or as £0.45. Never write both a £ sign and a p, like £0.45p.

pencil45pbook£3.05ruler£1.20bag£12.99
Price tags. £3.05 means 3 pounds and 5 pence.

Changing between pounds and pence. To change pounds to pence, multiply by 100: £2.07 = 207p. To change pence to pounds, divide by 100 (the digits move two places to the right, as in Section 6.4): 345p = £3.45. 7p = £0.07 (you need the 0 in the tenths place).

Adding up coins. Count how much each kind of coin is worth in pence, then add the amounts.

£150p20p20p10p5p2p
100p + 50p + 20p + 20p + 10p + 5p + 2p = 207p = £2.07.

Comparing money. To compare amounts, change them to the same unit first. £3.40 and 304p: £3.40 = 340p. 340p is more than 304p, so £3.40 > 304p. Fewest coins. To make an amount with the fewest coins, take the biggest coin that fits, then the biggest coin that fits what is left, and so on.

Key words. Pence (p) are small amounts of money. Pounds (£) are bigger. Change to a different unit means to write the same amount in another unit.

Key ideas

  • 100p = £1.
  • Money has two digits after the decimal point: £3.05, £4.50.
  • Pence to pounds: divide by 100. Pounds to pence: multiply by 100.
  • 7p = £0.07, not £0.7. And £4.5 should be £4.50.
  • Never write £ and p together.
  • To compare money, change everything to pence first.
Worked example 6.6.1
How much money is shown? Write the total in pounds.
£150p20p20p10p5p2p

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Count how much each kind of coin or note is worth in pence. Add the amounts. Then write the total in pounds and pence.

  1. Count each kind of note and coin. Group the same ones together. Change each group into pence.
    1 × £1 = 100p
    1 × 50p = 50p
    2 × 20p = 40p
    1 × 10p = 10p
    1 × 5p = 5p
    1 × 2p = 2p
  2. Add the groups, biggest first. Adding the big amounts first is easier. Keep a running total.
    100p
    100p + 50p = 150p
    150p + 40p = 190p
    190p + 10p = 200p
    200p + 5p = 205p
    205p + 2p = 207p
  3. Write the total. 100p = £1, so change to pounds and pence if it is 100p or more.
    207p = £2.07

Check. Add in a different order, smallest first: 2p + 5p + 10p + 20p + 20p + 50p + 100p = 207p. ✓

Watch out. Change everything to pence first. Do not add pounds and pence together as if they were the same.

Worked example 6.6.2
Write 345p in pounds.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Divide the pence by 100 to find the pounds. The pence left over go after the decimal point, with two digits.

  1. Remember: 100 pence make 1 pound. So we divide the pence by 100 to find the pounds.
    345 ÷ 100 = 3 remainder 45
  2. Write the pounds and the pence. 3 pounds and 45p.
    3 pounds and 45p
  3. Put them together with a decimal point. The pence always get two digits after the decimal point.
    £3.45

Check. Go back: £3.45 = 3 × 100 + 45 = 345p. ✓

Watch out. Money always has two digits after the decimal point.

Worked example 6.6.3
Write 7p in pounds.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Divide the pence by 100 to find the pounds. The pence left over go after the decimal point, with two digits.

  1. Remember: 100 pence make 1 pound. So we divide the pence by 100 to find the pounds.
    7 ÷ 100 = 0 remainder 7
  2. Write the pounds and the pence. The amount is less than 100p, so there are no whole pounds.
    0 pounds and 7p
  3. Put them together with a decimal point. The pence always get TWO digits: write a 0 in front if there is only one.
    £0.07   (the 0 holds the tens-of-pence place)

Check. Go back: £0.07 = 0 × 100 + 7 = 7p. ✓

Watch out. Do not write £0.7: money always has two digits after the point.

Worked example 6.6.4
Write £2.07 in pence.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Multiply the pounds by 100 and add the pence.

  1. Remember: 1 pound is 100 pence. So we multiply the pounds by 100.
    2 × 100 = 200p
  2. Add the pence. The two digits after the decimal point are the pence.
    200p + 7p = 207p
  3. Write the answer with the unit p. Pence are written with a small p after the number.
    £2.07 = 207p

Check. Go back: 207p ÷ 100 = £2.07. ✓

Watch out. £2.07 is 207p, not 27p: if the pence are less than 10, put a 0 in: £2.07 = 207p.

Worked example 6.6.5
Write < or > in the box.   £3.40  [ ]   304p

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Change both amounts into the same unit (pence). Then compare the numbers.

  1. Change both amounts to pence. We can only compare money when it is in the same unit. To change pounds to pence, multiply by 100.
    £3.40 = 340p  (£3 × 100 + 40 = 340)
    304p = 304p
  2. Compare the numbers of pence. The bigger number of pence is the bigger amount.
    340 > 304
  3. Write the answer.
    £3.40 > 304p

Check. Picture £3.40 and 304p as coins: more money in the first. ✓

Watch out. Do not compare 3.40 with 304 as they are. Change to the same unit first: 340p and 304p.

Worked example 6.6.6
Write these amounts in order, smallest first.   £1.20,   95p,   £1.05,   110p

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Change every amount to pence. Put the numbers in order. Then write the amounts the way they were first written.

  1. Change every amount to pence. The amounts are in different units, so we change them all to pence (£1 = 100p).
    £1.20 = 120p
    95p = 95p
    £1.05 = 105p
    110p = 110p
  2. Put the numbers of pence in order. We want smallest first.
    95p, 105p, 110p, 120p
  3. Write the original amounts in that order. Use the way each amount was written in the question.
    95p,  £1.05,  110p,  £1.20

Check. Count them: 4 amounts in the question and 4 in the answer. ✓

Watch out. Do not mix up pence and pounds: 95p is less than £1.05 even though 95 is bigger than 1.05.

Worked example 6.6.7
What are the fewest coins that make £1.87?

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Start with the biggest coin that fits. Take it away, then do the same with what is left. Keep going until nothing is left.

  1. Take the biggest coin that is not more than 187p. Using the biggest coins each time gives the fewest coins.
    Take £1.   187p − 100p = 87p left
  2. Take the biggest coin that is not more than 87p. Using the biggest coins each time gives the fewest coins.
    Take 50p.   87p − 50p = 37p left
  3. Take the biggest coin that is not more than 37p. Using the biggest coins each time gives the fewest coins.
    Take 20p.   37p − 20p = 17p left
  4. Take the biggest coin that is not more than 17p. Using the biggest coins each time gives the fewest coins.
    Take 10p.   17p − 10p = 7p left
  5. Take the biggest coin that is not more than 7p. Using the biggest coins each time gives the fewest coins.
    Take 5p.   7p − 5p = 2p left
  6. Take the biggest coin that is not more than 2p. Using the biggest coins each time gives the fewest coins.
    Take 2p.   2p − 2p = 0p left
  7. Write the coins. Check the amount: they should add up to £1.87.
    £1, 50p, 20p, 10p, 5p, 2p (6 coins)

Check. Add the coins: 100p + 50p + 20p + 10p + 5p + 2p = 187p = £1.87. ✓

Watch out. Do not use lots of small coins. Always take the biggest coin that fits.

Watch out

Two digits for the pence. £5.05 is 5 pounds and 5 pence. £5.5 would mean £5.50. And when you compare, do not compare 95 with 1.05 as they are: change to the same unit. 95p is LESS than £1.05 even though 95 is a bigger number than 1.05.

Exercise 6F  Money: pounds and pence

Non-calculator
1
FHow much money is shown? Write each total using £ or p.
(a)
50p20p10p5p2p1p
Total =
(b)
£2£150p50p20p
Total =
(c)
£10£5£120p20p5p
Total =
2
FQuick-fire! Write each amount in pounds.
(a)250p =
(b)605p =
(c)90p =
(d)7p =
(e)1205p =
(f)480p =
3
FQuick-fire! Write each amount in pence.
(a)£4.20 =
(b)£0.65 =
(c)£6.05 =
(d)£0.08 =
(e)£12.30 =
(f)£3.00 =
4
FWrite each amount using a pound sign and a decimal point.
(a)3 pounds and 40 pence =
(b)5 pounds and 5 pence =
(c)65 pence =
(d)12 pounds and 9 pence =
5
FEach amount is written wrongly. Write it correctly.
(a)£4.5 (meant: four pounds fifty) should be
(b)£5.5 (meant: five pounds five pence) should be
(c)£0.45p (meant: forty-five pence) should be
(d)£20.3 (meant: twenty pounds thirty pence) should be
6
FWrite <, > or = in each box.
(a)£2.50  [ ]   250p
(b)£3.05  [ ]   350p
(c)99p  [ ]   £1.00
(d)£1.75  [ ]   157p
(e)£0.60  [ ]   6p
7
FWrite the amounts in order.
(a)Smallest first: £2.50,  199p,  £2.05,  90p
(b)Biggest first: £3.05,  £0.03,  35p,  350p
8
FLook at the price tags.
pen85pbook£2.40ruler£1.15rubber60p
(a)Which item costs the most?
(b)Which item costs the least?
(c)Write the prices in order, biggest first.
9
FWrite the fewest coins that make each amount.
(a)38p =
(b)74p =
(c)£1.43 =
10
FHow many coins make each total?
(a)How many 20p coins make £3?
(b)How many 50p coins make £8?
(c)How many 5p coins make £2?
11
PSZainab has a piggy bank with 2 £1 coins, 3 50p coins, 5 20p coins and 4 10p coins. How much money is in the piggy bank?
£1£150p50p50p20p20p20p20p20p10p10p10p10p
12
RMei says, “I can make exactly 47p using only 5p coins and 10p coins.” Is she right? Explain.
13
RJack has 3 coins. They are worth exactly 35p in total. Which three coins does he have?
14
RShow three different ways to make £1 using exactly five coins.
6.7

Adding, subtracting and money problems

Year 4
Add and subtract money, Change, Multi-step money problems, Simple measure problems with decimals

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Adding, subtracting and money problemsComing soon

Adding money. Write the amounts in columns with the decimal points in a straight line, so pounds are under pounds and pence are under pence. Add the pence first, then the pounds. If the pence make 100p or more, carry 1 to the pounds, as you do with any column addition (Chapter 2).

For example, to add £2.75 and £1.86 we write the numbers like this. The decimal points are in a straight line.

£110p1p
£2.75
+ £1.86
£ .  

A good check is to estimate: round each amount to the nearest pound. £2.75 is about £3 and £1.86 is about £2, so the total is about £5.

Another way. Add the pounds and the pence separately. £3.85 + £2.47: pounds 3 + 2 = 5. Pence 85 + 47 = 132p = £1.32. Then £5 + £1.32 = £6.32.

Subtracting money is the same as column subtraction: the bigger amount goes on top. If the pence are too small, exchange 1 pound for 100p.

Here is £8.30 − £4.65 set out in columns.

£110p1p
£ 8. 3 0
− £4.65
£ .  

Change. The change is the money you get back when you pay with more than the cost. Change = money paid − total cost. You can subtract, or count up from the cost to the money paid: first to the next whole pound, then up in whole pounds.

£13.40£14.00£20.00+60p+£6
£20 − £13.40: count up 60p to £14, then £6 to £20. The change is 60p + £6 = £6.60.

Multiplying and sharing. For 3 items that cost £1.35 each, multiply the pounds and the pence separately: 3 × £1 = £3 and 3 × 35p = 105p = £1.05. The total is £4.05. To share £7.20 equally between 4 people, change to pence: 720p ÷ 4 = 180p = £1.80 each.

Measures with decimals. You can add and subtract lengths, masses and capacities written as decimals in the same way. Line up the decimal points. 2.5 m has one decimal place and 1.75 m has two, so write 2.5 as 2.50. Then 2.50 + 1.75 = 4.25 m.

Multi-step problems. Draw a bar model. Work out what you need to find first, and do the calculations in order.

£2.55£1.50?£10
A bar model: £10 is split into the cost of two things and the change.

Key words. The total is all the amounts added together. Change is the money you get back. To estimate is to find an approximate answer by rounding. Carry and exchange are column-method tricks.

Key ideas

  • Line up the decimal points. Pounds under pounds, pence under pence.
  • Add or subtract the pence first, then the pounds. Carry or exchange when you need to.
  • Change = money paid − total cost. You can also count up from the cost.
  • Multiply the pounds and the pence separately. Change 100p into £1.
  • To share money equally, change to pence and divide. Change back to pounds.
  • Estimate first: round each amount to the nearest pound to check the answer.
Worked example 6.7.1
Work out £2.75 + £1.86.

Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.

Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.

  1. Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
    £110p1p
    £2.75
    + £1.86
    £ .  
  2. Add the pence. Always start on the right.
    5 + 6 = 11
    11 is 10 or more. Write 1 in the pence column and carry 1 to the tens of pence column.
  3. Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.
    7 + 8 + 1 = 16
    16 is 10 or more. Write 6 in the tens of pence column and carry 1 to the pounds column (across the decimal point).
  4. Add the pounds. Now the next column to the left. Add the 1 we carried as well.
    2 + 1 + 1 = 4
    4 is less than 10, so write 4. There is nothing to carry.
  5. Read the answer. Put the decimal point in the answer, directly under the other decimal points.
    £110p1p
    £2.75
    + £1.86
    £4.61
    11

    £2.75 + £1.86 = £4.61

Check. Estimate: round to the nearest pound: £3 + £2 = £5. This is close to £4.61. ✓

Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.

Worked example 6.7.2
Work out £3.85 + £2.47. Add the pounds and pence separately.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Add the pounds, then add the pence. If the pence make 100p or more, change 100p into another pound.

  1. Split each amount into pounds and pence. We add the pounds and the pence separately.
    £3.85 = £3 + 85p
    £2.47 = £2 + 47p
  2. Add the pounds. Add the whole pound parts.
    £3 + £2 = £5
  3. Add the pence. Add the pence parts.
    85p + 47p = 132p
  4. Change 100 pence into a pound. The pence total is 100p or more. Every 100p is £1.
    132p = £1 and 32p
    £5 + £1 = £6
  5. Put the pounds and pence together.
    £6 and 32p = £6.32

Check. Estimate: round to the nearest pound: £4 + £2 = £6. This is close to £6.32. ✓

Watch out. If the pence add up to more than 100p, you must change 100p into £1. Do not write £5.113.

Worked example 6.7.3
Work out £8.30 − £4.65.

Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.

Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.

  1. Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
    £110p1p
    £ 8. 3 0
    − £4.65
    £ .  
  2. Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.
    0 is not enough to take away 5. We need to exchange.
    Exchange 1 from the tens of pence column: 3 becomes 2, and the pence column goes from 0 to 10.
    10 − 5 = 5
  3. Exchange, then subtract the tens of pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.
    2 is not enough to take away 6. We need to exchange.
    (There were 3 in this column to start with, but we gave one away in an earlier exchange.)
    Exchange 1 from the pounds column: 8 becomes 7, and the tens of pence column goes from 2 to 12. (This crosses the decimal point.)
    12 − 6 = 6
  4. Subtract the pounds. Now the next column to the left.
    (This digit is 7 now, not 8, because we exchanged from this column.)
    7 − 4 = 3
  5. Read the answer. Put the decimal point in the answer, directly under the other decimal points.
    £110p1p
    £78.123100
    − £4.65
    £3.65

    £8.30 − £4.65 = £3.65

Check. Add back: £3.65 + £4.65 = £8.30. ✓
Estimate: £8 − £5 = £3, close to £3.65.

Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.

Worked example 6.7.4
Work out £10.00 − £4.35.

Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.

Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.

  1. Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
    £10£110p1p
    £ 1 0. 0 0
    − £4.35
    £  .  
  2. Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.
    0 is not enough to take away 5. We need to exchange.
    The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
    Exchange 1 from the tens of pounds column: 1 becomes 0, and the pounds column goes from 0 to 10.
    Exchange 1 from the pounds column: 10 becomes 9, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
    Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 0 to 10.
    10 − 5 = 5
  3. Subtract the tens of pence. Now the next column to the left.
    (This digit is 9 now, not 0, because we exchanged from this column.)
    9 − 3 = 6
  4. Subtract the pounds. Now the next column to the left.
    (This digit is 9 now, not 0, because we exchanged from this column.)
    9 − 4 = 5
  5. Bring down the tens of pounds digit. The bottom number has no digit in this column.
    (This digit is 0 now, not 1, because we exchanged from this column.)
    Nothing to take away here, so the digit stays: 0.
  6. Read the answer. Put the decimal point in the answer, directly under the other decimal points.
    £10£110p1p
    £0190.90100
    − £4.35
    £ 5.65

    £10.00 − £4.35 = £5.65

Check. Add back: £5.65 + £4.35 = £10.00. ✓
Estimate: £10 − £4 = £6, close to £5.65.

Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.

Worked example 6.7.5
Mia buys a pencil for £1.45 and a rubber for 65p. She pays with a £5 note. How much change does she get?

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.

  1. Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
    £1.45£0.65?£5.00
  2. Step 1: find the total cost. Add all the prices.
    £1.45 + £0.65 = £2.10
    £110p1p
    £1.45
    + £0.65
    £2.10
    11
  3. Step 2: find the change. Take the cost away from the money paid.
    £5.00 − £2.10 = £2.90
    £110p1p
    £45.100 0
    − £2.10
    £2.90
  4. Write the answer.
    The change is £2.90

Check. Add the change to the cost: £2.10 + £2.90 = £5.00, the money paid. ✓

Watch out. Take away the TOTAL cost, not just one price.

Worked example 6.7.6
A book costs £13.40. Noah pays with a £20 note. Count up to find his change.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Count up from the cost to the money paid. First jump to the next whole pound, then jump in whole pounds. Add the jumps.

  1. Start at the cost. We count up from what we spent to the money we paid. The jumps add up to the change.
    Start at £13.40
  2. Jump up to the next whole pound. This makes the next jump easier.
    £13.40 + 60p = £14.00
  3. Jump up to the money paid. Count on in whole pounds.
    £14.00 + £6 = £20.00
  4. Draw the jumps on a number line.
    £13.40£14.00£20.00+60p+£6
  5. Add up the jumps. The total of the jumps is the change.
    60p + £6 = £6.60

Check. Subtract: £20.00 − £13.40 = £6.60. ✓

Watch out. Keep the jumps small and friendly: pence to the next pound, then pounds.

Worked example 6.7.7
A bun costs £1.35. How much do 3 buns cost?

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Multiply the pounds and the pence separately. Change any pence over 100p into pounds. Then add the parts.

  1. Split the price into pounds and pence. It is easier to multiply each part.
    £1.35 = £1 + 35p
  2. Multiply the pounds. 3 lots of £1.
    £1 × 3 = £3
  3. Multiply the pence. 3 lots of 35p.
    35p × 3 = 105p
  4. Change the pence into pounds. 100p = £1.
    105p = £1 and 5p = £1.05
  5. Add the parts together.
    £3 + £1.05 = £4.05

Check. Estimate: £1.35 is about £1, and 3 × £1 = £3, close to £4.05. ✓

Watch out. Write the answer with two decimal places, and change pence over 100p into pounds.

Worked example 6.7.8
Four friends share a bill of £7.20 equally. How much does each friend pay?

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Change the money into pence. Divide by the number of shares. Change the answer back to pounds and pence.

  1. Change the amount to pence. Pence are whole numbers, so they are easier to divide.
    £7.20 = 720p
  2. Divide by 4. Sharing equally into 4 means dividing by 4.
    720p ÷ 4 = 180p
  3. Change back to pounds and pence. 100p = £1.
    180p = £1.80

Check. Go back: £1.80 × 4 = £7.20. ✓

Watch out. Do not divide the pounds and pence as if they were one number. Change to pence first.

Worked example 6.7.9
Aisha buys 3 pens at 85p each and a notebook for £1.50. She pays with a £10 note. How much change does she get?

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Find the cost of each group of items. Add them to find the total. Then take the total away from the money paid to find the change.

  1. Find the cost of 3 pens. 3 lots of £0.85.
    3 × £0.85 = £2.55  (85p × 3 = 255p)
  2. Add the costs to find the total. Use a column method, with the decimal points lined up.
    £2.55 + £1.50 = £4.05
    £110p1p
    £2.55
    + £1.50
    £4.05
    1
  3. Take the total cost away from the money paid. What is left is the change.
    £10.00 − £4.05 = £5.95
    £10£110p1p
    £0190.90100
    − £4.05
    £ 5.95
  4. Write the answer.
    The change is £5.95

Check. Add the change to the total: £4.05 + £5.95 = £10.00. ✓

Watch out. Multiply first, then add, then subtract from the money paid.

Worked example 6.7.10
A bag of potatoes has a mass of 1.75 kg. A bag of carrots has a mass of 2.5 kg. What is the total mass?

Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.

Method. Line up the decimal points. Add column by column from the right. Carry when a column makes 10 or more. Write the unit.

  1. Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.
    2.5 = 2.50
  2. Line up the amounts in columns. Put the decimal points in a straight line, so tenths are under tenths and ones under ones.
    Oth
    1.75
    + 2.50
     .  
  3. Add the hundredths. Always start on the right.
    5 + 0 = 5
    5 is less than 10, so write 5. There is nothing to carry.
  4. Add the tenths. Now the next column to the left.
    7 + 5 = 12
    12 is 10 or more. Write 2 in the tenths column and carry 1 to the ones column (across the decimal point).
  5. Add the ones. Now the next column to the left. Add the 1 we carried as well.
    1 + 2 + 1 = 4
    4 is less than 10, so write 4. There is nothing to carry.
  6. Read the answer. Put the decimal point in the answer, directly under the other decimal points.
    Oth
    1.75
    + 2.50
    4.25
    1

    1.75 kg + 2.50 kg = 4.25 kg

Check. Take away: 4.25 kg − 2.50 kg = 1.75 kg. ✓

Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.

Worked example 6.7.11
A plank is 3.2 m long. Dev saws off 1.45 m. How long is the plank now?

Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.

Method. Line up the decimal points with the bigger number on top. Subtract column by column from the right. Exchange when a top digit is too small. Write the unit.

  1. Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.
    3.2 = 3.20
  2. Line up the amounts in columns. The bigger number goes on top. Put the decimal points in a straight line.
    Oth
     3. 2 0
    − 1.45
     .  
  3. Exchange, then subtract the hundredths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.
    0 is not enough to take away 5. We need to exchange.
    Exchange 1 from the tenths column: 2 becomes 1, and the hundredths column goes from 0 to 10.
    10 − 5 = 5
  4. Exchange, then subtract the tenths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.
    1 is not enough to take away 4. We need to exchange.
    (There were 2 in this column to start with, but we gave one away in an earlier exchange.)
    Exchange 1 from the ones column: 3 becomes 2, and the tenths column goes from 1 to 11. (This crosses the decimal point.)
    11 − 4 = 7
  5. Subtract the ones. Now the next column to the left.
    (This digit is 2 now, not 3, because we exchanged from this column.)
    2 − 1 = 1
  6. Read the answer. Put the decimal point in the answer, directly under the other decimal points.
    Oth
    23.112100
    − 1.45
    1.75

    3.20 m − 1.45 m = 1.75 m

Check. Add back: 1.75 m + 1.45 m = 3.20 m. ✓

Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.

Watch out

Line up the decimal points, not the last digits. £5 + £2.35 must be written £5.00 + £2.35. And if the pence add up to more than 99p, change 100p into £1: £3.65 + £2.48 is £6.13, not £5.113.

Exercise 6G  Adding, subtracting and change

Non-calculator
1
FAdd. Write each answer in pounds and pence.
(a)£1.30 + £2.45 =
(b)£4.20 + £3.55 =
(c)£2.75 + £1.24 =
(d)£5.60 + £2.10 =
2
FAdd. The pence will make more than 100p, so you must carry.
(a)£3.65 + £2.48 =
(b)£4.79 + £2.86 =
(c)£5.95 + £1.27 =
(d)£3.58 + £3.64 =
3
FAdd the pounds and the pence separately.
(a)£4.65 + £2.78 =
(b)£5.70 + £3.55 =
(c)£2.49 + £1.98 =
4
FSubtract. Write each answer in pounds and pence.
(a)£7.85 − £3.40 =
(b)£9.50 − £4.25 =
(c)£6.98 − £2.35 =
(d)£8.40 − £5.20 =
5
FSubtract. You will need to exchange.
(a)£8.20 − £3.65 =
(b)£7.05 − £2.38 =
(c)£6.00 − £2.75 =
(d)£12.00 − £8.45 =
6
FAdd the three amounts.
(a)£1.45 + £2.30 + £0.65 =
(b)£3.99 + £2.50 + £1.99 =
7
FHow much more money is needed to make the total? Find the missing amount.
(a)£4.50 + ? = £7.00
(b)£6.75 + ? = £10.00
(c)£3.65 + ? = £5.00
(d)£8.45 + ? = £12.00
8
FWork out the change from each payment.
(a)Pay with £5. The cost is £3.65. Change =
(b)Pay with £10. The cost is £7.45. Change =
(c)Pay with £20. The cost is £12.50. Change =
(d)Pay with £5. The cost is £1.99. Change =
9
PSZara buys a sandwich and a juice. She pays with a £10 note. How much change does she get?
sandwich£2.85juice95p
10
PSDev has £12. He buys a bag for £4.50 and a cap for £6.75. How much money does he have left?
£4.50£6.75?£12
11
RZainab wants to buy a book for £3.95 and a card for £2.10.
(a)Estimate the total by rounding each price to the nearest pound.
(b)Work out the exact total.
(c)How much more is the exact total than the estimate?
12
RJack says, “£3.65 + £2.48 = £5.113.” What mistake has Jack made? What is the correct total?
13
RWhich two of these items cost exactly £5 together?   £1.35, £2.20, £2.80, £3.15 and £1.95.
kite£1.35ball£2.20book£2.80game£3.15puzzle£1.95

Exercise 6H  Multiplying, sharing and measures

Non-calculator
1
FWork out the cost of each group of items.
(a)3 × £1.20 =
(b)4 × £2.50 =
(c)2 × £3.45 =
(d)5 × £0.65 =
2
FShare the money equally. How much does each person get?
(a)£6.80 ÷ 2 =
(b)£9.60 ÷ 4 =
(c)£8.40 ÷ 3 =
3
FWork out each fraction of the money.
(a)12 of £8 =
(b)14 of £10 =
(c)34 of £6 =
4
FAdd the measures. Line up the decimal points.
(a)1.5 kg + 2.25 kg =
(b)0.75 m + 1.5 m =
(c)2.4 litres + 1.35 litres =
5
FSubtract the measures. Line up the decimal points.
(a)4.5 m − 1.25 m =
(b)5 kg − 2.75 kg =
(c)2.1 litres − 0.85 litres =
6
PSLeo buys 4 stickers at 35p each and a comic for £2.20. He pays with a £5 note. How much change does he get?
sticker35pcomic£2.20
7
PSA cinema ticket costs £4.75. How much do 4 tickets cost?
8
PSMei wants to buy a game that costs £12.60. She has £4.20 and saves £2.10 each week. How many weeks will it take her to have enough money?
£4.20£2.10 a week?£12.60
9
PSA ribbon is 5 m long. Priya cuts off a piece 1.75 m long. Then she cuts off a piece 2.5 m long.
1.75 m2.5 m?5 m
(a)How much ribbon has she cut off in total?
(b)How much ribbon is left?
10
PSFour friends share the £9.60 cost of a pizza equally. Amira also buys a drink for £1.35.
(a)How much does each friend pay for the pizza?
(b)How much does Amira spend altogether?
11
RZara has £10. She wants to buy a book for £2.95, a game for £3.20 and a toy for £3.55. Prove that she has enough money.
book£2.95game£3.20toy£3.55
12
RMia has 7 coins. Each coin is a 50p coin or a 20p coin. The coins are worth £2.60 in total. How many 50p coins and how many 20p coins does she have?
13
RLeo says, “3 × £1.45 = £3.135.” What mistake has Leo made? What is the correct answer?

Chapter summary

SkillMethod
Tenths1/10 = 0.1. The first digit after the decimal point is tenths. 7/10 = 0.7. 10 tenths = 1 whole: 0.9 + 0.1 = 1.0. 2 4/10 = 2.4.
Hundredths1/100 = 0.01. The second digit after the point is hundredths. 37/100 = 0.37. 10 hundredths = 1 tenth. Use a 0 to keep the place: 7/100 = 0.07.
Fractions ↔ decimalsTenths: count one digit after the point (bottom number 10). Hundredths: two digits (bottom number 100). 0.63 = 63/100, 2.3 = 2 3/10.
Place valueOnes . tenths hundredths. In 3.45: 3 ones, 4 tenths (0.4), 5 hundredths (0.05). 3.45 = 3 + 0.4 + 0.05.
CountingCount in 0.1 or 0.01. 0.8, 0.9, 1.0, 1.1. 0.08, 0.09, 0.10, 0.11. Keep the same number of decimal places.
Halves and quarters1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75 (50, 25 and 75 squares of a hundred square). 2 1/2 = 2.5.
Dividing by 10 and 100÷ 10: digits move 1 column right. ÷ 100: digits move 2 columns right. Fill empty columns with 0: 7 ÷ 100 = 0.07.
Comparing and orderingLine up the decimal points. Compare from the left: ones, tenths, hundredths. 0.45 < 0.5 (45 hundredths < 50 hundredths).
Rounding to a whole numberLook at the tenths digit. 5 or more: round up. 4 or less: round down. 3.4 ≈ 3, 3.5 ≈ 4, 3.7 ≈ 4.
Pounds and pence100p = £1. Money has two digits after the point: £3.05. Pence to pounds: ÷ 100. Pounds to pence: × 100. Never write £ and p together.
Comparing moneyChange to the same unit (pence) first. £3.40 = 340p, which is more than 304p.
Adding and subtracting moneyLine up the decimal points. Pence first, then pounds. Carry 100p as £1 or exchange £1 for 100p. Estimate to check.
ChangeChange = money paid − total cost. Or count up from the cost to the next pound, then to the money paid.
Multiplying and sharing moneyMultiply the pounds and the pence separately and change pence over 99 to pounds. To share, change to pence and divide.
Measures with decimalsLine up the decimal points and write 2.5 as 2.50 to add or subtract: 2.50 + 1.75 = 4.25. Cm ÷ 100 = m, mm ÷ 10 = cm.

Can you…?

  • I can write tenths and hundredths as fractions and as decimals.
  • I know the value of each digit in a number with up to two decimal places.
  • I can show decimals on a place-value chart, a hundred square and a number line.
  • I can count up and down in tenths and hundredths, including across a whole number.
  • I know 1/2 = 0.5, 1/4 = 0.25 and 3/4 = 0.75.
  • I can divide a one- or two-digit number by 10 and by 100 and write the answer as a decimal.
  • I can compare and order decimals with up to two decimal places.
  • I can round a decimal with one decimal place to the nearest whole number.
  • I can write amounts of money correctly, change between pounds and pence, and compare money.
  • I can add and subtract money using columns, and work out change.
  • I can multiply and share money and solve multi-step money problems.
  • I can add and subtract measures written as decimals.

Key terms

Decimal
A number with a decimal point, like 3.45. The digits after the point are parts of a whole.
Decimal point
The dot that separates the whole numbers from the parts of a whole.
Tenth
One of 10 equal parts of a whole: 1/10 = 0.1.
Hundredth
One of 100 equal parts of a whole: 1/100 = 0.01.
Decimal place
A column after the decimal point. 0.47 has two decimal places.
Place value
The value of a digit because of the column it is in.
Hundred square
A square cut into 100 small squares. Each small square is one hundredth.
Equivalent
Having the same value, like 1/2 and 0.5.
Compare
To say which of two numbers is bigger or smaller.
Order
To put numbers in a list, smallest first or biggest first.
Round
To change a number to a nearby number that is easier to use, like 3.6 to 4.
Pence (p)
Small units of money. 100p = £1.
Pound (£)
A unit of money. £1 = 100p.
Change
The money you get back when you pay with more than the cost.
Total
All the amounts added together.
Estimate
To find an approximate answer by rounding the numbers first.
Convert
To change an amount from one unit to another, like cm to m.

Exercise 6Z  Check-up (non-calculator)

Non-calculator
1
What decimal is shaded?
2
Write 7100 as a decimal.
3
Write 0.75 as a fraction in its simplest form.
4
What is the value of the digit 3 in the number 5.38?
5
Work out 56 ÷ 100.
6
Write these numbers in order, smallest first.   0.61,   0.16,   0.66
7
Round 6.7 to the nearest whole number.
8
Write 605p in pounds.
9
A hat costs £3.85. Ben pays with a £10 note. How much change does he get?
10
A rope is 3.5 m long. Tom cuts off 1.75 m. How long is the rope now?

Total 17 marks. Allow about 17 minutes.

Exercise 6X  SATs-style questions

Non-calculator
1
FWhat decimal is shaded?[1 mark]
2
FWork out 84 ÷ 10.[1 mark]
3
FWhat is the value of the digit 7 in the number 6.72?[1 mark]
4
FRound 12.6 to the nearest whole number.[1 mark]
5
RWhich two of these are equal to 12? Tick two boxes.
A 0.5    B 0.05    C 510    D 0.25[2 marks]
6
FWrite these numbers in order, smallest first.   4.35,   4.53,   4.05
Show how you know.[2 marks]
7
FWrite £6.05 in pence.[1 mark]
8
RAisha says, “0.65 is bigger than 0.7, because 65 is bigger than 7.” Is Aisha correct? Explain how you know.[2 marks]
9
PSPriya buys 3 apples at 45p each and a loaf of bread for £1.20. She pays with a £5 note. How much change does she get?   Show your working.[3 marks]
apple45ploaf£1.20
10
PSA ribbon is 3.5 m long. Zara cuts off a piece 1.25 m long and then a piece 0.75 m long. How much ribbon is left?   Show your working.[3 marks]
1.25 m0.75 m?3.5 m
← Chapter 5: FractionsChapter 7: Length, mass, capacity, perimeter and area →

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