Year 4: Hundredths and place value
Part of the Year 4 tenths, hundredths and money chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Hundredths and place value
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.
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.
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.
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)
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.
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.
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.
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.
- 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
- 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 - Write the fraction. The top number is the shaded squares.
37 100 - Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.
ones tenths hundredths 0.37 0 . 3 7
37 hundredths = 0 ones, 3 tenths and 7 hundredths, so 0.37
Check. Go back: 0.37 is
Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.
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.
- Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
7 100 - 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
- Look at the picture.
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths hundredths 0.07 0 . 0 7 - Write the decimal.
7 100
Check. Go back to a fraction: 0.07 =
Watch out. 7 hundredths is 0.07, not 0.7. The 0 in the tenths column keeps the 7 in the hundredths column.
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.
- 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.
- 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.
- Write the fraction. 0.63 =
63 100
Check. Go back:
Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.
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.
- Draw a place-value table. The columns are ones, then tenths, then hundredths.
ones tenths hundredths 8.04 8 . 0 4 - 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
- 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.
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.
- Write the number in a place-value table.
ones tenths hundredths 5.82 5 . 8 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 - 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.
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.
- 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)
- 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
- 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.
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.
- 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.
- Work out what one gap is worth. Share the distance between the ends equally.0.1 ÷ 10 = 0.01
- 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.
- 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-calculatorKey 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.
- 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
- Count the shaded squares. Count the full rows first (10 squares each), then the extra squares.2 full rows = 20 squares
20 + 3 = 23 squares - Write the fraction. The top number is the shaded squares.
23 100 - Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.
ones tenths hundredths 0.23 0 . 2 3
23 hundredths = 0 ones, 2 tenths and 3 hundredths, so 0.23
Check. Go back: 0.23 is
Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.
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.
- 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
- Count the shaded squares. Count the full rows first (10 squares each), then the extra squares.5 full rows = 50 squares
50 + 8 = 58 squares - Write the fraction. The top number is the shaded squares.
58 100 - Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.
ones tenths hundredths 0.58 0 . 5 8
58 hundredths = 0 ones, 5 tenths and 8 hundredths, so 0.58
Check. Go back: 0.58 is
Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.
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.
- 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
- Count the shaded squares. Count the shaded squares.7 squares
- Write the fraction. The top number is the shaded squares.
7 100 - Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.
ones tenths hundredths 0.07 0 . 0 7
7 hundredths = 0 ones, 0 tenths and 7 hundredths, so 0.07
Check. Go back: 0.07 is
Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.
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.
- Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
9 100 - Notice there are no tenths. 9 hundredths is less than 1 tenth (1 tenth = 10 hundredths). The tenths column must hold a 0.0 tenths and 9 hundredths
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths hundredths 0.09 0 . 0 9 - Write the decimal.
9 100
Check. Go back to a fraction: 0.09 =
Watch out. 7 hundredths is 0.07, not 0.7. The 0 in the tenths column keeps the 7 in the hundredths column.
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.
- Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
45 100 - Split the hundredths into tenths and hundredths. 10 hundredths make 1 tenth.45 hundredths = 4 tenths and 5 hundredths
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths hundredths 0.45 0 . 4 5 - Write the decimal.
45 100
Check. Go back to a fraction: 0.45 =
Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.
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.
- Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
70 100 - Split the hundredths into tenths and hundredths. 10 hundredths make 1 tenth.70 hundredths = 7 tenths and 0 hundredths
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths hundredths 0.70 0 . 7 0 - Write the decimal.
70 100
Check. Go back to a fraction: 0.70 =
Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.
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.
- Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
3 100 - Notice there are no tenths. 3 hundredths is less than 1 tenth (1 tenth = 10 hundredths). The tenths column must hold a 0.0 tenths and 3 hundredths
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths hundredths 0.03 0 . 0 3 - Write the decimal.
3 100
Check. Go back to a fraction: 0.03 =
Watch out. 7 hundredths is 0.07, not 0.7. The 0 in the tenths column keeps the 7 in the hundredths column.
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.
- Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
99 100 - Split the hundredths into tenths and hundredths. 10 hundredths make 1 tenth.99 hundredths = 9 tenths and 9 hundredths
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths hundredths 0.99 0 . 9 9 - Write the decimal.
99 100
Check. Go back to a fraction: 0.99 =
Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.
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.
- Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
12 100 - Split the hundredths into tenths and hundredths. 10 hundredths make 1 tenth.12 hundredths = 1 tenth and 2 hundredths
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths hundredths 0.12 0 . 1 2 - Write the decimal.
12 100
Check. Go back to a fraction: 0.12 =
Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.
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.
- Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.0.21 has 2 digits after the point, so the bottom number is 100.
- 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 21, which is 21.
- Write the fraction. 0.21 =
21 100
Check. Go back:
Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.
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.
- Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.0.08 has 2 digits after the point, so the bottom number is 100.
- 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 08, which is 8.
- Write the fraction. 0.08 =
8 100
Check. Go back:
Watch out. For 0.05 the top number is 5, not 05. The bottom number is 100 because there are two digits after the point.
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.
- Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.0.60 has 2 digits after the point, so the bottom number is 100.
- 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 60, which is 60.
- Write the fraction. 0.60 =
60 100
Check. Go back:
Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.
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.
- Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.0.99 has 2 digits after the point, so the bottom number is 100.
- 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 99, which is 99.
- Write the fraction. 0.99 =
99 100
Check. Go back:
Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.
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.
- Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.0.35 has 2 digits after the point, so the bottom number is 100.
- 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 35, which is 35.
- Write the fraction. 0.35 =
35 100
Check. Go back:
Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.
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.
- Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.0.04 has 2 digits after the point, so the bottom number is 100.
- 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 04, which is 4.
- Write the fraction. 0.04 =
4 100
Check. Go back:
Watch out. For 0.05 the top number is 5, not 05. The bottom number is 100 because there are two digits after the point.
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. Count the counters in each column. Each column has its own value.
- Count the counters in the ones column. Ones counters are worth 1 each.0 ones
- Count the counters in the tenths column. Tenths counters are worth 0.1 each.3 tenths
- Count the counters in the hundredths column. Hundredths counters are worth 0.01 each. If the column is empty, the digit is 0.4 hundredths
- Write the number. Put the digits in order with the decimal point after the ones.0 ones, 3 tenths and 4 hundredths = 0.34
Check. Read it back: 0.34 is 0 ones, 3 tenths and 4 hundredths. ✓
Watch out. An empty column means a 0 digit. Do not leave it out.
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. Count the counters in each column. Each column has its own value.
- Count the counters in the ones column. Ones counters are worth 1 each.1 one
- Count the counters in the tenths column. Tenths counters are worth 0.1 each.5 tenths
- Count the counters in the hundredths column. Hundredths counters are worth 0.01 each. If the column is empty, the digit is 0.2 hundredths
- Write the number. Put the digits in order with the decimal point after the ones.1 one, 5 tenths and 2 hundredths = 1.52
Check. Read it back: 1.52 is 1 one, 5 tenths and 2 hundredths. ✓
Watch out. An empty column means a 0 digit. Do not leave it out.
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. Count the counters in each column. Each column has its own value.
- Count the counters in the ones column. Ones counters are worth 1 each.2 ones
- Count the counters in the tenths column. Tenths counters are worth 0.1 each.0 tenths
- Count the counters in the hundredths column. Hundredths counters are worth 0.01 each. If the column is empty, the digit is 0.7 hundredths
- Write the number. Put the digits in order with the decimal point after the ones.2 ones, 0 tenths and 7 hundredths = 2.07
Check. Read it back: 2.07 is 2 ones, 0 tenths and 7 hundredths. ✓
Watch out. An empty column means a 0 digit. Do not leave it out.
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.
- Draw a place-value table. The columns are ones, then tenths, then hundredths.
ones tenths hundredths 4.26 4 . 2 6 - 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.4 ones, 2 tenths and 6 hundredths
- Write the number. Put the decimal point between the ones and the tenths.4.26
Check. Read it back: 4.26 is 4 ones, 2 tenths and 6 hundredths. ✓
Watch out. Do not leave out a 0. Two ones, no tenths and 7 hundredths is 2.07, not 2.7.
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.
- Draw a place-value table. The columns are ones, then tenths, then hundredths.
ones tenths hundredths 0.09 0 . 0 9 - 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.0 ones, 0 tenths and 9 hundredths
- Write the number. Put the decimal point between the ones and the tenths.0.09
Check. Read it back: 0.09 is 0 ones, 0 tenths and 9 hundredths. ✓
Watch out. Do not leave out a 0. Two ones, no tenths and 7 hundredths is 2.07, not 2.7.
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.
- Draw a place-value table. The columns are ones, then tenths, then hundredths.
ones tenths hundredths 7.05 7 . 0 5 - 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.7 ones, 0 tenths and 5 hundredths
- Write the number. Put the decimal point between the ones and the tenths.7.05
Check. Read it back: 7.05 is 7 ones, 0 tenths and 5 hundredths. ✓
Watch out. Do not leave out a 0. Two ones, no tenths and 7 hundredths is 2.07, not 2.7.
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.
- Draw a place-value table. The columns are ones, then tenths, then hundredths.
ones tenths hundredths 2.91 2 . 9 1 - 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.2 ones, 9 tenths and 1 hundredth
- Write the number. Put the decimal point between the ones and the tenths.2.91
Check. Read it back: 2.91 is 2 ones, 9 tenths and 1 hundredth. ✓
Watch out. Do not leave out a 0. Two ones, no tenths and 7 hundredths is 2.07, not 2.7.
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.
- Draw a place-value table. The columns are ones, then tenths, then hundredths.
ones tenths hundredths 0.60 0 . 6 0 - 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.0 ones, 6 tenths and 0 hundredths
- Write the number. Put the decimal point between the ones and the tenths.0.60
Check. Read it back: 0.60 is 0 ones, 6 tenths and 0 hundredths. ✓
Watch out. Do not leave out a 0. Two ones, no tenths and 7 hundredths is 2.07, not 2.7.
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. Find which column the digit is in. The value is the digit times the value of that column.
- Write the number in a place-value table. This shows which column each digit is in.
ones tenths hundredths 3.47 3 . 4 7 - Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.The digit 7 is in the hundredths column.
- Work out its value. One hundredth is worth 0.01. The digit tells us how many of them there are.7 × 0.01 = 0.07
- Write the answer. 7 hundredths (0.07)
Check. Check by adding up all the parts: they should make 3.47. ✓
Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.
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. Find which column the digit is in. The value is the digit times the value of that column.
- Write the number in a place-value table. This shows which column each digit is in.
ones tenths hundredths 5.82 5 . 8 2 - Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.The digit 8 is in the tenths column.
- Work out its value. One tenth is worth 0.1. The digit tells us how many of them there are.8 × 0.1 = 0.8
- Write the answer. 8 tenths (0.8)
Check. Check by adding up all the parts: they should make 5.82. ✓
Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.
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. Find which column the digit is in. The value is the digit times the value of that column.
- Write the number in a place-value table. This shows which column each digit is in.
ones tenths hundredths 0.91 0 . 9 1 - Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.The digit 9 is in the tenths column.
- Work out its value. One tenth is worth 0.1. The digit tells us how many of them there are.9 × 0.1 = 0.9
- Write the answer. 9 tenths (0.9)
Check. Check by adding up all the parts: they should make 0.91. ✓
Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.
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. Find which column the digit is in. The value is the digit times the value of that column.
- Write the number in a place-value table. This shows which column each digit is in.
ones tenths hundredths 6.05 6 . 0 5 - Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.The digit 5 is in the hundredths column.
- Work out its value. One hundredth is worth 0.01. The digit tells us how many of them there are.5 × 0.01 = 0.05
- Write the answer. 5 hundredths (0.05)
Check. Check by adding up all the parts: they should make 6.05. ✓
Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.
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. Find which column the digit is in. The value is the digit times the value of that column.
- Write the number in a place-value table. This shows which column each digit is in.
ones tenths hundredths 7.28 7 . 2 8 - Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.The digit 7 is in the ones column.
- Work out its value. One one is worth 1. The digit tells us how many of them there are.7 × 1 = 7
- Write the answer. 7 ones (7)
Check. Check by adding up all the parts: they should make 7.28. ✓
Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.
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. Find which column the digit is in. The value is the digit times the value of that column.
- Write the number in a place-value table. This shows which column each digit is in.
tens ones tenths hundredths 12.34 1 2 . 3 4 - Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.The digit 1 is in the tens column.
- Work out its value. One ten is worth 10. The digit tells us how many of them there are.1 × 10 = 10
- Write the answer. 1 ten (10)
Check. Check by adding up all the parts: they should make 12.34. ✓
Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.
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. Count the columns from the decimal point to find the tenths column.
- Write the number in a place-value table. Each digit goes in its own column. The decimal point sits between the ones and the tenths.
ones tenths hundredths 6.72 6 . 7 2 - Find the tenths column. Tenths is the first column after the decimal point.The digit is 7.
Check. In 6.72 the digit 7 is worth 7 tenths. ✓
Watch out. Tenths is the FIRST digit after the point, hundredths is the SECOND.
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. Count the columns from the decimal point to find the hundredths column.
- Write the number in a place-value table. Each digit goes in its own column. The decimal point sits between the ones and the tenths.
ones tenths hundredths 0.58 0 . 5 8 - Find the hundredths column. Hundredths is the second column after the decimal point.The digit is 8.
Check. In 0.58 the digit 8 is worth 8 hundredths. ✓
Watch out. Tenths is the FIRST digit after the point, hundredths is the SECOND.
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. Count the columns from the decimal point to find the tenths column.
- Write the number in a place-value table. Each digit goes in its own column. The decimal point sits between the ones and the tenths.
ones tenths hundredths 9.04 9 . 0 4 - Find the tenths column. Tenths is the first column after the decimal point.The digit is 0.
Check. In 9.04 the digit 0 is worth 0 tenths. ✓
Watch out. Tenths is the FIRST digit after the point, hundredths is the SECOND.
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. Count the columns from the decimal point to find the hundredths column.
- Write the number in a place-value table. Each digit goes in its own column. The decimal point sits between the ones and the tenths.
ones tenths hundredths 3.19 3 . 1 9 - Find the hundredths column. Hundredths is the second column after the decimal point.The digit is 9.
Check. In 3.19 the digit 9 is worth 9 hundredths. ✓
Watch out. Tenths is the FIRST digit after the point, hundredths is the SECOND.
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.
- Write the number in a place-value table.
ones tenths hundredths 3.45 3 . 4 5 - Work out the value of each digit. A zero digit is worth nothing, so we can leave it out.3 ones = 3
4 tenths = 0.4
5 hundredths = 0.05 - Write the parts as an addition. 3.45 = 3 + 0.4 + 0.05
Check. Add the parts: 3 + 0.4 + 0.05 = 3.45. ✓
Watch out. Write 0.4 for 4 tenths, not 4. Write 0.05 for 5 hundredths, not 0.5.
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.
- Write the number in a place-value table.
ones tenths hundredths 6.08 6 . 0 8 - Work out the value of each digit. A zero digit is worth nothing, so we can leave it out.6 ones = 6
8 hundredths = 0.08 - Write the parts as an addition. 6.08 = 6 + 0.08
Check. Add the parts: 6 + 0.08 = 6.08. ✓
Watch out. Write 0.4 for 4 tenths, not 4. Write 0.05 for 5 hundredths, not 0.5.
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.
- Write the number in a place-value table.
ones tenths hundredths 0.72 0 . 7 2 - Work out the value of each digit. A zero digit is worth nothing, so we can leave it out.7 tenths = 0.7
2 hundredths = 0.02 - Write the parts as an addition. 0.72 = 0.7 + 0.02
Check. Add the parts: 0.7 + 0.02 = 0.72. ✓
Watch out. Write 0.4 for 4 tenths, not 4. Write 0.05 for 5 hundredths, not 0.5.
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.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.0.04 to 0.05: the jump is 0.01 (1 hundredth)
- 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 1.00.0.04, 0.05, 0.06, 0.07, 0.08, 0.09
- Write the missing numbers. 0.06, 0.09
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.
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.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.0.97 to 0.98: the jump is 0.01 (1 hundredth)
- 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 1.00.0.97, 0.98, 0.99, 1.00, 1.01, 1.02
- Write the missing numbers. 0.99, 1.01
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.
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 hundredths, one jump at a time.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.0.13 to 0.12: the jump is 0.01 (1 hundredth)
- Count back in hundredths. Going back, 0.10 is the same as 10 hundredths, so before 0.10 comes 0.09. And 1.00 is 100 hundredths, so before 1.00 comes 0.99.0.13, 0.12, 0.11, 0.10, 0.09, 0.08
- Write the missing numbers. 0.11, 0.09
Check. Count back 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.
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.
- 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 0.5 to 0.6 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.0.1 ÷ 10 = 0.01
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 2 gaps after 0.5.
- Work out the number. Start at the left end and add the gaps.0.5 + 2 × 0.01 = 0.5 + 0.02 = 0.52
Check. Count back from 0.6: 8 gaps back is 0.6 − 0.08 = 0.52. ✓
Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.
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.
- 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 0.5 to 0.6 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.0.1 ÷ 10 = 0.01
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 5 gaps after 0.5.
- Work out the number. Start at the left end and add the gaps.0.5 + 5 × 0.01 = 0.5 + 0.05 = 0.55
Check. Count back from 0.6: 5 gaps back is 0.6 − 0.05 = 0.55. ✓
Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.
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.
- 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 0.5 to 0.6 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.0.1 ÷ 10 = 0.01
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 8 gaps after 0.5.
- Work out the number. Start at the left end and add the gaps.0.5 + 8 × 0.01 = 0.5 + 0.08 = 0.58
Check. Count back from 0.6: 2 gaps back is 0.6 − 0.02 = 0.58. ✓
Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.
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. Change each column into hundredths, then add them.
- Split the number into its columns. Each digit is worth a different amount.0.3 = 0 ones and 3 tenths
- Change each part into hundredths. 1 whole = 100 hundredths and 1 tenth = 10 hundredths.3 tenths = 3 × 10 = 30 hundredths
0 hundredths
0 + 30 + 0 = 30 hundredths - Write the answer. 30 hundredths
Check. 30 hundredths written as a decimal is 0.3. ✓
Watch out. 1 whole is 10 tenths, but it is 100 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. Change each column into hundredths, then add them.
- Split the number into its columns. Each digit is worth a different amount.0.8 = 0 ones and 8 tenths
- Change each part into hundredths. 1 whole = 100 hundredths and 1 tenth = 10 hundredths.8 tenths = 8 × 10 = 80 hundredths
0 hundredths
0 + 80 + 0 = 80 hundredths - Write the answer. 80 hundredths
Check. 80 hundredths written as a decimal is 0.8. ✓
Watch out. 1 whole is 10 tenths, but it is 100 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. Change each column into hundredths, then add them.
- Split the number into its columns. Each digit is worth a different amount.1.5 = 1 one and 5 tenths
- Change each part into hundredths. 1 whole = 100 hundredths and 1 tenth = 10 hundredths.1 whole one = 1 × 100 = 100 hundredths
5 tenths = 5 × 10 = 50 hundredths
0 hundredths
100 + 50 + 0 = 150 hundredths - Write the answer. 150 hundredths
Check. 150 hundredths written as a decimal is 1.5. ✓
Watch out. 1 whole is 10 tenths, but it is 100 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. Change each column into hundredths, then add them.
- Split the number into its columns. Each digit is worth a different amount.2.04 = 2 ones, 0 tenths and 4 hundredths
- Change each part into hundredths. 1 whole = 100 hundredths and 1 tenth = 10 hundredths.2 whole ones = 2 × 100 = 200 hundredths
0 tenths = 0 × 10 = 0 hundredths
4 hundredths
200 + 0 + 4 = 204 hundredths - Write the answer. 204 hundredths
Check. 204 hundredths written as a decimal is 2.04. ✓
Watch out. 1 whole is 10 tenths, but it is 100 hundredths.
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. There are 100 cm in 1 m, so 1 cm is one hundredth of a metre.
- Write the length as hundredths of a metre. 1 cm is 1/100 m.17 cm =
17 100 - Write it as a decimal. 17 hundredths: 0 ones, 1 tenth and 7 hundredths.
17 100
Check. 0.17 × 100 = 17. ✓
Watch out. Keep the unit. A small number of cm is a small part of a metre, so the decimal is less than 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. There are 100 cm in 1 m, so 1 cm is one hundredth of a metre.
- Write the length as hundredths of a metre. 1 cm is 1/100 m.4 cm =
4 100 - Write it as a decimal. 4 hundredths: 0 ones, 0 tenths and 4 hundredths.
4 100
Check. 0.04 × 100 = 4. ✓
Watch out. Keep the unit. A small number of cm is a small part of a metre, so the decimal is less than 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. There are 100 cm in 1 m, so 1 cm is one hundredth of a metre.
- Write the length as hundredths of a metre. 1 cm is 1/100 m.85 cm =
85 100 - Write it as a decimal. 85 hundredths: 0 ones, 8 tenths and 5 hundredths.
85 100
Check. 0.85 × 100 = 85. ✓
Watch out. Keep the unit. A small number of cm is a small part of a metre, so the decimal is less than 1.
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. Draw both numbers on hundred squares and compare how many squares are shaded.
- Shade 0.5. 0.5 is 5 tenths, which is 5 full rows.5 × 10 = 50 squares
- Shade 0.05. 0.05 is 5 hundredths, which is just 5 small squares.5 squares
- Compare. 50 squares is not the same as 5 squares, so 0.5 is ten times bigger.
0.5
0.05
Check. 0.05 × 10 = 0.5. ✓
Watch out. The 0 in 0.05 is in the tenths column, so the 5 is worth 5 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. The number is between 0.3 and 0.4, so the tenths digit is 3. The hundredths digit is double the tenths digit.
- Find the tenths digit. Between 0.3 and 0.4 means 3 tenths and some hundredths.tenths digit = 3
- Find the hundredths digit. It is double the tenths digit.3 × 2 = 6
- Write the number. 0 ones, 3 tenths and 6 hundredths.0.36
Check. 0.36 is between 0.3 and 0.4 and 6 is double 3. ✓
Watch out. Check all the clues at the end.