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Step-by-step practice: Maths · Level 5Chapter 7 · Decimals to tenths and hundredths
Level 5 · Chapter 7

Decimals to tenths and hundredths

By the end of this chapter you will be able to

  • Write and read decimals to two places
  • Say the value of the tenths and hundredths digits
  • Place a hundredths number on a 0 to 1 number line
  • Compare and order decimals to hundredths
  • Round decimals, and add and subtract money and lengths

You should already know

  • Decimals to tenths (chapter 1)
  • Fractions with the same denominator (chapter 6)

Where this leads

  • Decimals and place value in more detail (a later level)

Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Read and write decimals to two places, equivalent to tenths and hundredths (Y4 and Y5 paraphrase), Say the value of each digit in a decimal to hundredths (Y5 paraphrase), Compare and order decimals to two places, and write 0.5 as 0.50 (Y5 paraphrase), Round decimals to the nearest whole number, tenth and hundredth (Y5 paraphrase), Solve money and length problems with decimals to hundredths (Y5 paraphrase).

Exercise P  Do you remember?

Non-calculator
1
FWhat is 1/10 of 50?
2
FWrite 3 + 4/10 as a decimal.
3
FWork out 4,625 + 1,380.
4
FWhat is 3/4 + 1/4? Write it in its simplest form.
5
FWhich is greater: 5/8 or 3/8?
7.1

Hundredths as decimals

Level 5
Read and write decimals to two places, equivalent to hundredths, Write a decimal with tenths and hundredths
Video lesson: Hundredths as decimalsComing soon

A hundredth is one of 100 equal parts. Two places after the decimal point show hundredths: 7/100 = 0.07.

The first place after the point is tenths; the second place is hundredths. 3 + 4/10 + 7/100 = 3.47.

Key ideas

  • Two places after the point: the first is tenths, the second is hundredths.
  • 7/100 = 0.07, not 0.7.
  • Put a zero in the tenths place when there are no tenths.
Worked example 7.1.1
Write 7/100 as a decimal.

Method. Hundredths have two places after the decimal point.

  1. Look at the bottom number. The bottom number 100 means hundredths: two places after the point.
    7/100
  2. Write the digits in the two places. 7 hundredths: a 0 in the tenths place, then 7 in the hundredths place.
    0.07
  3. Write the answer. The two digits after the point are hundredths.
    0.07

Check. Check: 0.07 is 7 hundredths, which is 7/100.

Watch out. Keep both places. 7/100 is 0.07, not 0.7.

Worked example 7.1.2
Write 3 + 4/10 + 7/100 as a decimal.

Method. Write the whole number, then one digit for the tenths and two digits for the hundredths.

  1. Write the whole number first. This is the part before the decimal point.
    3
  2. Write the tenths and the hundredths after the point. 4/10 is one place, and 7/100 is two places.
    3.47
  3. Write the answer. Check that each digit is in the right place.
    3.47

Check. Check: 3.47 = 3 + 0.4 + 0.07, when h is a single digit.

Watch out. Use two places for hundredths. The hundredths digit is the second place after the point.

Worked example 7.1.3
What is the value of the hundredths digit in 4.56?

Method. The second digit after the point is the number of hundredths.

  1. Find the hundredths digit. It is the second digit after the decimal point.
    The digit is 6
  2. Write its value. 6 hundredths is 6/100.
    6/100 = 0.06
  3. Write the answer. The value is a decimal with the digit in the second place.
    0.06

Check. Check: in 4.56 the second digit after the point is 6, so the value is 6/100 = 0.06.

Watch out. The value is 0.0 with the digit after it: 0.07, not 0.7.

Watch out

Watch out. 0.7 is 7 tenths, and 0.07 is 7 hundredths. They are not the same number.

Exam tip

Grown-up tip. Use 100 small squares or 10 by 10 grid paper. Ask the child to shade 7 squares and write the decimal.

Exercise 7A  Practice: hundredths as decimals

Non-calculator
1
FWrite 3 + 1/10 + 6/100 as a decimal.
2
FWrite 5 + 7/10 + 5/100 as a decimal.
3
FWhat is the value of the hundredths digit in 3.56?
4
FWrite 73/100 as a decimal.
5
FWrite 79/100 as a decimal.
6
FWrite 7 + 4/10 + 8/100 as a decimal.
7
FWhat is the value of the hundredths digit in 8.03?
8
FWhat is the value of the hundredths digit in 5.92?
9
FWrite 5 + 7/10 + 6/100 as a decimal.
10
FWhat is the value of the hundredths digit in 9.98?
11
FWrite 8 + 7/10 + 5/100 as a decimal.
12
FWrite 5 + 9/10 + 4/100 as a decimal.
13
FWrite 2 + 8/10 + 2/100 as a decimal.
14
FWhat is the value of the hundredths digit in 2.57?
15
FWrite 2 + 5/10 + 9/100 as a decimal.
16
FWrite 3 + 1/10 + 5/100 as a decimal.
7.2

The value of each digit, and the 0 to 1 number line

Level 5
Say the value of each digit in a decimal to hundredths, Place a hundredths number on a 0 to 1 number line
Video lesson: The value of each digit, and the 0 to 1 number lineComing soon

Each digit after the point has a value. In 4.56, the 5 is 5 tenths (0.5) and the 6 is 6 hundredths (0.06).

On a number line from 0 to 1, the tenths are the big marks and the hundredths are the small marks between them.

00.10.20.30.40.50.60.70.80.91?
A number line from 0 to 1 with hundredths; the mark shows 0.56

Key ideas

  • The first digit after the point is tenths.
  • The second digit after the point is hundredths.
  • Ten hundredths make one tenth.
Worked example 7.2.1
What is the value of the tenths digit in 4.56?

Method. The first digit after the point is the number of tenths.

  1. Find the tenths digit. It is the first digit after the decimal point.
    The digit is 5
  2. Write its value. 5 tenths is 5/10.
    5/10 = 0.5
  3. Write the answer. The value of the tenths digit is 0.1 times the digit.
    0.5

Check. Check: the first digit after the point is 5, so the value is 5/10 = 0.5.

Watch out. Read the digit after the point as tenths. 4 tenths is 0.4, not 4.

Worked example 7.2.2
The orange mark shows a decimal between 0 and 1. Write the decimal to two places.

Method. Find the tenths, then count the hundredths beyond them.

  1. Find the tenths either side. Read the tenths labels to find the gap.
    The mark is between 0.30 and 0.40
  2. Count the small steps. Each small step is one hundredth.
    7 hundredths past 0.30
  3. Write the decimal. Two places after the point.
    0.37

Check. Check: 0.37 is 37 hundredths, which is 37/100.

Watch out. There are ten small steps between two tenths marks, so each small step is a hundredth.

Worked example 7.2.3
The orange mark shows a decimal between 0 and 1. Write the decimal to two places.

Method. Find the tenths, then count the hundredths beyond them.

  1. Find the tenths either side. Read the tenths labels to find the gap.
    The mark is between 0.60 and 0.70
  2. Count the small steps. Each small step is one hundredth.
    4 hundredths past 0.60
  3. Write the decimal. Two places after the point.
    0.64

Check. Check: 0.64 is 64 hundredths, which is 64/100.

Watch out. There are ten small steps between two tenths marks, so each small step is a hundredth.

Watch out

Watch out. The 5 in 4.56 is 0.5, not 5. The value depends on the place it is in.

Exam tip

Grown-up tip. Ask: “How many small steps are between 0.3 and 0.4?” The answer is ten, so each step is a hundredth.

Exercise 7B  Practice: digits and the number line

Non-calculator
1
FThe orange mark shows a decimal between 0 and 1. Write the decimal to two places.
00.10.20.30.40.50.60.70.80.91?
2
FThe orange mark shows a decimal between 0 and 1. Write the decimal to two places.
00.10.20.30.40.50.60.70.80.91?
3
FWhat is the value of the hundredths digit in 7.71?
4
FThe orange mark shows a decimal between 0 and 1. Write the decimal to two places.
00.10.20.30.40.50.60.70.80.91?
5
FWhat is the value of the tenths digit in 8.25?
6
FWhat is the value of the hundredths digit in 7.44?
7
FWhat is the value of the tenths digit in 7.68?
8
FWhat is the value of the tenths digit in 6.26?
9
FWhat is the value of the tenths digit in 6.72?
10
FWhat is the value of the tenths digit in 8.83?
11
FWhat is the value of the hundredths digit in 4.35?
12
FWhat is the value of the tenths digit in 2.74?
13
FWhat is the value of the tenths digit in 3.11?
14
FWhat is the value of the tenths digit in 4.42?
15
FWhat is the value of the hundredths digit in 1.03?
16
FWhat is the value of the hundredths digit in 5.37?
7.3

Equal decimals, comparing and ordering

Level 5
Write 0.5 as 0.50 and say why they are equal, Compare and order decimals to hundredths
Video lesson: Equal decimals, comparing and orderingComing soon

Adding a zero at the end of a decimal does not change its value. 0.5 = 0.50, because 5 tenths is the same as 50 hundredths.

To compare decimals, look at the whole numbers, then the tenths, then the hundredths.

Key ideas

  • A zero at the end does not change the value: 0.5 = 0.50.
  • Compare the whole numbers first, then tenths, then hundredths.
  • Order from the smallest by comparing each place.
Worked example 7.3.1
Write 0.5 with two decimal places.

Method. A zero at the end of a decimal does not change its value.

  1. Add a zero at the end. Adding a zero after the last digit does not change the value.
    0.5 = 0.50
  2. Compare the two numbers. The tenths digit and the zero in the hundredths are both empty places.
    0.50 = 0.5
  3. Write the answer. They are equal; the zero only shows that there are no hundredths.
    0.50

Check. Check: 5/10 = 50/100.

Watch out. 0.5 and 0.50 are equal. The zero at the end does not make the number bigger.

Worked example 7.3.2
Which is greater: 0.45 or 0.50?

Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.

  1. Compare the whole numbers. The bigger whole number is the bigger decimal.
    0 and 0
  2. Compare the tenths. If the whole numbers match, the tenths decide.
    4 and 5 tenths
  3. Compare the hundredths. If the tenths also match, the hundredths decide.
    5 and 0 hundredths
  4. Choose the greater number. This is the number with the larger digit in the first place they differ.
    0.50

Check. Check: 0.50 is 50 hundredths and 0.45 is 45 hundredths.

Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.

Worked example 7.3.3
Put these in order, smallest first: 0.47, 0.04, 0.50, 4.05.

Method. Compare the whole numbers, then the tenths, then the hundredths.

  1. Compare the whole numbers. Put the smallest whole number first.
    0, 0, 0, 4
  2. Compare the tenths and hundredths. Use the next places to put the rest in order.
    0.47, 0.04, 0.50, 4.05
  3. Write the list smallest first. Check each pair in order.
    0.04, 0.47, 0.50, 4.05

Check. Check: each number is smaller than the one after it.

Watch out. Do not order by the number of digits. Compare the places from the left.

Watch out

Watch out. 0.45 is less than 0.5, even though 45 is more than 5. Compare the tenths first.

Exam tip

Grown-up tip. Ask: “Which is greater, 0.6 or 0.58?” Then ask why the tenths decide before the hundredths.

Exercise 7C  Practice: equal decimals, comparing and ordering

Non-calculator
1
FWrite 5.6 with two decimal places.
2
FWhich is greater: 5.94 or 6.73?
3
FWhich is greater: 6.23 or 2.79?
4
FPut these in order, smallest first: 6.97, 2.74, 3.52, 9.82.
5
FPut these in order, smallest first: 8.29, 4.48, 8.84, 4.20.
6
FWhich is greater: 3.68 or 3.41?
7
FPut these in order, smallest first: 5.60, 7.33, 8.61, 7.56.
8
FWrite 9.1 with two decimal places.
9
FPut these in order, smallest first: 2.13, 6.78, 8.67, 6.07.
10
FWhich is greater: 8.11 or 3.12?
11
FPut these in order, smallest first: 6.87, 4.11, 2.99, 4.08.
12
FWhich is greater: 6.43 or 8.43?
13
FWhich is greater: 1.91 or 3.23?
14
FWhich is greater: 4.29 or 6.68?
15
FWhich is greater: 8.14 or 5.25?
16
FWhich is greater: 2.34 or 5.27?
7.4

Rounding decimals

Level 5
Round decimals to the nearest whole number, tenth and hundredth
Video lesson: Rounding decimalsComing soon

Look at the digit after the place you are rounding to. 5 or more: round up. 4 or less: round down.

To round to the nearest tenth, look at the hundredths. To round to the nearest whole number, look at the tenths.

Key ideas

  • Round to the nearest whole number: look at the tenths digit.
  • Round to the nearest tenth: look at the hundredths digit.
  • Round to the nearest hundredth: look at the thousandths digit.
Worked example 7.4.1
Round 3.460 to the nearest whole number.

Method. Look at the digit after the place you are rounding to, then decide.

  1. Look at the tenths digit. This digit decides whether to round up or down.
    The digit is 4
  2. Decide. 5 or more: round up. 4 or less: round down.
    4 is 4 or less, so round down
  3. Write the rounded number. Make the digits after the rounding place zero, or leave them out.
    3

Check. Check: 3 is the closest number with the right number of places to 3.460.

Watch out. Round up only on a 5 or more. Do not drop the zero from the tenths when rounding to tenths.

Worked example 7.4.2
Round 4.560 to the nearest tenth.

Method. Look at the digit after the place you are rounding to, then decide.

  1. Look at the hundredths digit. This digit decides whether to round up or down.
    The digit is 6
  2. Decide. 5 or more: round up. 4 or less: round down.
    6 is 5 or more, so round up
  3. Write the rounded number. Make the digits after the rounding place zero, or leave them out.
    4.6

Check. Check: 4.6 is the closest number with the right number of places to 4.560.

Watch out. Round up only on a 5 or more. Do not drop the zero from the tenths when rounding to tenths.

Worked example 7.4.3
Round 4.876 to the nearest hundredth.

Method. Look at the digit after the place you are rounding to, then decide.

  1. Look at the thousandths digit. This digit decides whether to round up or down.
    The digit is 6
  2. Decide. 5 or more: round up. 4 or less: round down.
    6 is 5 or more, so round up
  3. Write the rounded number. Make the digits after the rounding place zero, or leave them out.
    4.88

Check. Check: 4.88 is the closest number with the right number of places to 4.876.

Watch out. Round up only on a 5 or more. Do not drop the zero from the tenths when rounding to tenths.

Watch out

Watch out. 3.46 to the nearest tenth is 3.5, not 3.4. Look at the hundredths digit, which is 6.

Exam tip

Grown-up tip. Ask: “Which digit decides? Is it 5 or more?” before the child writes the rounded number.

Exercise 7D  Practice: rounding decimals

Non-calculator
1
FRound 1.356 to the nearest tenth.
2
FRound 6.304 to the nearest whole number.
3
FRound 6.581 to the nearest tenth.
4
FRound 7.097 to the nearest tenth.
5
FRound 2.876 to the nearest whole number.
6
FRound 6.323 to the nearest whole number.
7
FRound 9.342 to the nearest hundredth.
8
FRound 3.399 to the nearest hundredth.
9
FRound 2.004 to the nearest hundredth.
10
FRound 1.629 to the nearest hundredth.
11
FRound 9.131 to the nearest tenth.
12
FRound 7.908 to the nearest tenth.
13
FRound 8.787 to the nearest hundredth.
14
FRound 2.312 to the nearest tenth.
15
FRound 4.649 to the nearest whole number.
16
FRound 3.528 to the nearest hundredth.
7.5

Adding and subtracting money and lengths

Level 5
Add and subtract decimals to hundredths in money and length problems
Video lesson: Adding and subtracting money and lengthsComing soon

Line up the decimal points, so that pounds are under pounds and pence are under pence. Add or subtract column by column, from the right.

Always write two places for pence: £5.00, not £5.

Key ideas

  • Line up the decimal points.
  • Add or subtract the pence first, then the pounds.
  • Keep the unit in the answer.
Worked example 7.5.1
Work out £3.46 + £2.85.

Method. Line up the decimal points and add in columns. Keep the pound sign and two places for pence.

  1. Line up the decimal points. Write the pounds and pence in columns.
    3.46 + 2.85
  2. Add the pence first. Carry any ten pence into the pounds.
    46 + 85 = 131 pence
  3. Add the pounds. Include any carried pounds.
    3 + 2 = 6 pounds
  4. Write the answer with the pound sign. Always write two places for the pence.
    £6.31

Check. Check: £6.31 - £2.85 = £3.46.

Watch out. Always write two digits for the pence: £5.00, not £5.

Worked example 7.5.2
Work out £5.00 - £2.36.

Method. Line up the decimal points, then subtract the pence and the pounds.

  1. Line up the decimal points. Write the amounts one above the other.
    5.00 - 2.36
  2. Subtract the pence, exchanging if needed. Take a pound to make 100 pence if the pence are too few.
    0 - 36 = 64 pence
  3. Subtract the pounds. Include any exchanged pound.
    2 pounds
  4. Write the answer with the pound sign. Two places for the pence.
    £2.64

Check. Check: £2.64 + £2.36 = £5.00.

Watch out. Always keep the decimal points in a line. Write £2.64, not £2.6.

Worked example 7.5.3
A rope is 1.25 m long. A second piece is 0.60 m long. What is the total length?

Method. Line up the decimal points, then add in columns, keeping the unit.

  1. Line up the decimal points. Add the metres and the centimetres in the right places.
    1.25 + 0.60
  2. Add the hundredths and tenths. Carry where needed.
    85 hundredths in total
  3. Write the total length with the unit. Give the answer in metres, to two places.
    1.85 m

Check. Check: 1.85 - 0.60 = 1.25.

Watch out. Write the unit in the answer: 1.85 m, not 1.85.

Watch out

Watch out. £5.00 - £2.36 is £2.64. Exchange a pound to make 100 pence first.

Exam tip

Grown-up tip. Use real coins. Ask the child to pay £2.36 with £5 and count the change.

Exercise 7E  Practice: money and lengths

Non-calculator
1
FWork out £5.41 + £4.82.
2
PSA rope is 2.33 m long. A second piece is 1.91 m long. What is the total length?
3
PSA rope is 1.56 m long. A second piece is 0.95 m long. What is the total length?
4
PSA rope is 1.10 m long. A second piece is 1.60 m long. What is the total length?
5
FWork out £7.37 - £3.77.
6
PSA rope is 1.55 m long. A second piece is 0.83 m long. What is the total length?
7
FWork out £2.14 + £6.92.
8
FWork out £5.58 - £2.34.
9
FWork out £7.67 + £3.79.
10
PSA rope is 1.50 m long. A second piece is 0.22 m long. What is the total length?
11
FWork out £5.02 - £3.57.
12
FWork out £4.70 + £4.63.
13
FWork out £5.96 + £1.63.
14
FWork out £3.55 + £4.40.
15
PSA rope is 1.74 m long. A second piece is 0.66 m long. What is the total length?
16
FWork out £4.64 + £6.49.

Chapter summary

SkillMethod
HundredthsTwo places after the point: tenths, then hundredths; 7/100 = 0.07
Digit valuesThe value depends on the place: 4.56 has 5 tenths and 6 hundredths
Equal decimalsA zero at the end does not change the value: 0.5 = 0.50
ComparingWhole numbers, then tenths, then hundredths
RoundingLook at the digit after the place; 5 or more rounds up
Money and lengthsLine up the points; add or subtract; keep two places for pence

Can you…?

  • I can read and write decimals to two places
  • I can say the value of the tenths and hundredths digits
  • I can place a hundredths number on a 0 to 1 number line
  • I can compare and order decimals to hundredths, and write 0.5 as 0.50
  • I can round decimals to the nearest whole number, tenth and hundredth
  • I can add and subtract money and lengths with decimals

Key terms

hundredth
one of 100 equal parts; written as 0.01 or as 1/100
decimal point
the dot that separates the whole number from the parts
round
make a number simpler, to the nearest place
value
what a digit is worth because of its place

Exercise 7Z  Check-up

Non-calculator
1
Work out £1.40 + £1.91.
2
Round 3.333 to the nearest tenth.
3
Write 9 + 8/10 + 3/100 as a decimal.
4
Round 4.170 to the nearest whole number.
5
The orange mark shows a decimal between 0 and 1. Write the decimal to two places.
00.10.20.30.40.50.60.70.80.91?
6
Write 2 + 3/10 + 9/100 as a decimal.
7
The orange mark shows a decimal between 0 and 1. Write the decimal to two places.
00.10.20.30.40.50.60.70.80.91?
8
A rope is 2.29 m long. A second piece is 2.16 m long. What is the total length?
9
Write 9.8 with two decimal places.
10
What is the value of the hundredths digit in 8.47?

Total 19 marks. Allow about 19 minutes.

Exercise 7X  Practice test questions

Non-calculator
1
FPut these in order, smallest first: 3.36, 3.62, 7.07, 8.81.[1 mark]
2
FRound 6.988 to the nearest hundredth.[1 mark]
3
FWhich is greater: 2.52 or 8.79?[1 mark]
4
FRound 2.129 to the nearest hundredth.[1 mark]
5
FRound 2.472 to the nearest whole number.[2 marks]
6
FWhat is the value of the hundredths digit in 4.55?[2 marks]
7
FWhat is the value of the hundredths digit in 1.07?[2 marks]
8
FWhat is the value of the hundredths digit in 2.75?[3 marks]
9
FPut these in order, smallest first: 1.84, 7.16, 7.13, 5.71.[3 marks]
10
FPut these in order, smallest first: 7.19, 2.71, 4.00, 2.82.[3 marks]
← Chapter 6: Adding and subtracting fractions with the same denominatorChapter 8: Metric length, mass and capacity →

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