Year 4: Tenths as decimals
Part of the Year 4 tenths, hundredths and money chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Tenths as decimals
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.
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.
On a number line. Between 0 and 1 there are 10 equal gaps. Each gap is one tenth, 0.1.
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.
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).
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.
- 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.
- Count the shaded parts. This gives the top number.7 parts are shaded, so the fraction is
7 10 - Write it as a decimal. Tenths go in the first column after the decimal point.
ones tenths 0.7 0 . 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
Watch out. Write the 0 ones before the decimal point: 0.7, not .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. 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. 10 means tenths. Tenths go in the first column after the decimal point.
4 10 - 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 0.4 0 . 4 - Write the decimal.
4 10
Check. Go back to a fraction: 0.4 =
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. 10 means tenths. Tenths go in the first column after the decimal point.2310 is 2 ones and 3 tenths.
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 2.3 2 . 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.
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.0.9 has 1 digit after the point, so the bottom number is 10.
- 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.
- Write the fraction. 0.9 =
9 10
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. 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 1 to 2 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.1 ÷ 10 = 0.1
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 4 gaps after 1.
- 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.
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.
- 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)
- 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
- 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.
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.
- 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)
- 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
- 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-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. Count the tenths that are shaded. Tenths are the first column after the decimal point.
- 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.
- Count the shaded parts. This gives the top number.3 parts are shaded, so the fraction is
3 10 - Write it as a decimal. Tenths go in the first column after the decimal point.
ones tenths 0.3 0 . 3
0 ones and 3 tenths = 0.3
Check. Go back to a fraction: 0.3 has 3 in the tenths column, so it is
Watch out. Write the 0 ones before the decimal point: 0.7, not .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. Count the tenths that are shaded. Tenths are the first column after the decimal point.
- 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.
- Count the shaded parts. This gives the top number.8 parts are shaded, so the fraction is
8 10 - Write it as a decimal. Tenths go in the first column after the decimal point.
ones tenths 0.8 0 . 8
0 ones and 8 tenths = 0.8
Check. Go back to a fraction: 0.8 has 8 in the tenths column, so it is
Watch out. Write the 0 ones before the decimal point: 0.7, not .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. Count the tenths that are shaded. Tenths are the first column after the decimal point.
- 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.
- Count the shaded parts. This gives the top number.5 parts are shaded, so the fraction is
5 10 - Write it as a decimal. Tenths go in the first column after the decimal point.
ones tenths 0.5 0 . 5
0 ones and 5 tenths = 0.5
Check. Go back to a fraction: 0.5 has 5 in the tenths column, so it is
Watch out. Write the 0 ones before the decimal point: 0.7, not .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. 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. 10 means tenths. Tenths go in the first column after the decimal point.
2 10 - Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 0.2 0 . 2 - Write the decimal.
2 10
Check. Go back to a fraction: 0.2 =
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. 10 means tenths. Tenths go in the first column after the decimal point.
5 10 - Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 0.5 0 . 5 - Write the decimal.
5 10
Check. Go back to a fraction: 0.5 =
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. 10 means tenths. Tenths go in the first column after the decimal point.
9 10 - Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 0.9 0 . 9 - Write the decimal.
9 10
Check. Go back to a fraction: 0.9 =
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. 10 means tenths. Tenths go in the first column after the decimal point.
1 10 - Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 0.1 0 . 1 - Write the decimal.
1 10
Check. Go back to a fraction: 0.1 =
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. 10 means tenths. Tenths go in the first column after the decimal point.
7 10 - Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 0.7 0 . 7 - Write the decimal.
7 10
Check. Go back to a fraction: 0.7 =
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. 10 means tenths. Tenths go in the first column after the decimal point.
4 10 - Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 0.4 0 . 4 - Write the decimal.
4 10
Check. Go back to a fraction: 0.4 =
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.0.3 has 1 digit after the point, so the bottom number is 10.
- 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 3, which is 3.
- Write the fraction. 0.3 =
3 10
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.0.7 has 1 digit after the point, so the bottom number is 10.
- 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 7, which is 7.
- Write the fraction. 0.7 =
7 10
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.0.1 has 1 digit after the point, so the bottom number is 10.
- 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 1, which is 1.
- Write the fraction. 0.1 =
1 10
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.0.9 has 1 digit after the point, so the bottom number is 10.
- 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.
- Write the fraction. 0.9 =
9 10
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.0.6 has 1 digit after the point, so the bottom number is 10.
- 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 6, which is 6.
- Write the fraction. 0.6 =
6 10
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.0.4 has 1 digit after the point, so the bottom number is 10.
- 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 4, which is 4.
- Write the fraction. 0.4 =
4 10
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. 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. 10 means tenths. Tenths go in the first column after the decimal point.1410 is 1 one and 4 tenths.
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 1.4 1 . 4 - Write the decimal. 1410 = 1.4
Check. Go back to a fraction: 1.4 = 1410. ✓
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. 10 means tenths. Tenths go in the first column after the decimal point.3710 is 3 ones and 7 tenths.
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 3.7 3 . 7 - Write the decimal. 3710 = 3.7
Check. Go back to a fraction: 3.7 = 3710. ✓
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. 10 means tenths. Tenths go in the first column after the decimal point.2110 is 2 ones and 1 tenth.
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 2.1 2 . 1 - Write the decimal. 2110 = 2.1
Check. Go back to a fraction: 2.1 = 2110. ✓
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. 10 means tenths. Tenths go in the first column after the decimal point.5910 is 5 ones and 9 tenths.
- Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.
ones tenths 5.9 5 . 9 - Write the decimal. 5910 = 5.9
Check. Go back to a fraction: 5.9 = 5910. ✓
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.1.5 has 1 digit after the point, so the bottom number is 10.
- 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 5, which is 5.
- Write the whole number in front. The 1 before the point stays as a whole number.1 and
5 10 - Write the fraction. 1.5 = 1510 (5 tenths)
Check. Go back: 1510 written as a decimal is 1.5. ✓
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.3.2 has 1 digit after the point, so the bottom number is 10.
- 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 2, which is 2.
- Write the whole number in front. The 3 before the point stays as a whole number.3 and
2 10 - Write the fraction. 3.2 = 3210 (2 tenths)
Check. Go back: 3210 written as a decimal is 3.2. ✓
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.4.8 has 1 digit after the point, so the bottom number is 10.
- 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 8, which is 8.
- Write the whole number in front. The 4 before the point stays as a whole number.4 and
8 10 - Write the fraction. 4.8 = 4810 (8 tenths)
Check. Go back: 4810 written as a decimal is 4.8. ✓
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.2.7 has 1 digit after the point, so the bottom number is 10.
- 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 7, which is 7.
- Write the whole number in front. The 2 before the point stays as a whole number.2 and
7 10 - Write the fraction. 2.7 = 2710 (7 tenths)
Check. Go back: 2710 written as a decimal is 2.7. ✓
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. 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 to 1 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.1 ÷ 10 = 0.1
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 2 gaps after 0.
- Work out the number. Start at the left end and add the gaps.0 + 2 × 0.1 = 0 + 0.2 = 0.2
Check. Count back from 1: 8 gaps back is 1 − 0.8 = 0.2. ✓
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 to 1 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.1 ÷ 10 = 0.1
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 6 gaps after 0.
- Work out the number. Start at the left end and add the gaps.0 + 6 × 0.1 = 0 + 0.6 = 0.6
Check. Count back from 1: 4 gaps back is 1 − 0.4 = 0.6. ✓
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 to 1 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.1 ÷ 10 = 0.1
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 9 gaps after 0.
- Work out the number. Start at the left end and add the gaps.0 + 9 × 0.1 = 0 + 0.9 = 0.9
Check. Count back from 1: 1 gap back is 1 − 0.1 = 0.9. ✓
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. Find the jump. Then count on in tenths, one jump at a time.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.0.2 to 0.3: the jump is 0.1 (1 tenth)
- Count on in tenths. 10 tenths make 1 whole, so after 0.9 comes 1.0.0.2, 0.3, 0.4, 0.5, 0.6, 0.7
- Write the missing numbers. 0.4, 0.6
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.
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.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.0.9 to 1.0: the jump is 0.1 (1 tenth)
- Count on in tenths. 10 tenths make 1 whole, so after 0.9 comes 1.0.0.7, 0.8, 0.9, 1.0, 1.1, 1.2
- Write the missing numbers. 0.8, 1.1
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.
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.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.1.4 to 1.5: the jump is 0.1 (1 tenth)
- Count on in tenths. 10 tenths make 1 whole, so after 0.9 comes 1.0.1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0
- Write the missing numbers. 1.7, 1.9
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.
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.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.0.9 to 0.8: the jump is 0.1 (1 tenth)
- Count back in tenths. Going back, 1.0 is the same as 10 tenths, so before 1.0 comes 0.9.0.9, 0.8, 0.7, 0.6, 0.5, 0.4
- Write the missing numbers. 0.7, 0.5
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.
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.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.0.9 to 0.8: the jump is 0.1 (1 tenth)
- Count back in tenths. Going back, 1.0 is the same as 10 tenths, so before 1.0 comes 0.9.1.3, 1.2, 1.1, 1.0, 0.9, 0.8
- Write the missing numbers. 1.2, 1.0
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.
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.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.2.1 to 2.0: the jump is 0.1 (1 tenth)
- Count back in tenths. Going back, 1.0 is the same as 10 tenths, so before 1.0 comes 0.9.2.1, 2.0, 1.9, 1.8, 1.7, 1.6, 1.5
- Write the missing numbers. 1.9, 1.6
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.
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 tenths, then add them.
- Split the number into its columns. Each digit is worth a different amount.0.6 = 0 ones and 6 tenths
- Change each part into tenths. 1 whole = 10 tenths.6 tenths
6 tenths - Write the answer. 6 tenths
Check. 6 tenths written as a decimal is 0.6. ✓
Watch out. Do not forget the whole ones: each one is worth 10 tenths.
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 tenths, then add them.
- Split the number into its columns. Each digit is worth a different amount.1.3 = 1 one and 3 tenths
- Change each part into tenths. 1 whole = 10 tenths.1 whole one = 1 × 10 = 10 tenths
3 tenths
10 + 3 = 13 tenths - Write the answer. 13 tenths
Check. 13 tenths written as a decimal is 1.3. ✓
Watch out. Do not forget the whole ones: each one is worth 10 tenths.
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 tenths, then add them.
- Split the number into its columns. Each digit is worth a different amount.2.5 = 2 ones and 5 tenths
- Change each part into tenths. 1 whole = 10 tenths.2 whole ones = 2 × 10 = 20 tenths
5 tenths
20 + 5 = 25 tenths - Write the answer. 25 tenths
Check. 25 tenths written as a decimal is 2.5. ✓
Watch out. Do not forget the whole ones: each one is worth 10 tenths.
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 tenths, then add them.
- Split the number into its columns. Each digit is worth a different amount.4.1 = 4 ones and 1 tenth
- Change each part into tenths. 1 whole = 10 tenths.4 whole ones = 4 × 10 = 40 tenths
1 tenth
40 + 1 = 41 tenths - Write the answer. 41 tenths
Check. 41 tenths written as a decimal is 4.1. ✓
Watch out. Do not forget the whole ones: each one is worth 10 tenths.
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 tenth of a metre is 0.1 m. Count how many tenths she uses.
- Find the size of one piece. The ribbon is cut into 10 equal pieces, so each piece is one tenth of a metre.1 piece =
1 10 - Count the pieces she uses. She uses 7 pieces.7 pieces = 7 tenths =
7 10 - Write it as a decimal. 7 tenths is 0 ones and 7 tenths.
7 10
Check. 10 pieces make 1 m. She uses 7 and has 3 left: 0.7 + 0.3 = 1.0. ✓
Watch out. Each piece is 0.1 m, not 1 m. Seven pieces is 0.7 m.
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. Each lap is one tenth of the race. Count the laps Tom has run.
- Find what one lap is worth. The race has 10 laps, so each lap is one tenth.1 lap =
1 10 - Count the laps run. 6 laps is 6 tenths.
6 10
Check. 0.6 has 6 in the tenths column. ✓
Watch out. The bottom number is all 10 laps, not the 6 laps Tom has run.
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. The laps left are the laps not yet run. Find how many tenths are left.
- Find the laps left. Take the laps run away from the 10 laps in the race.10 − 6 = 4 laps
- Write it as a decimal. 4 laps is 4 tenths.
4 10
Check. 0.6 + 0.4 = 1.0, the whole race. ✓
Watch out. 0.6 and 0.4 make 1 whole.
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. Write each one as a decimal. Look for the one that is worth a different amount.
- Write each as a decimal. 3/10 means 3 tenths. “Three tenths” is the same.
3 10 - Find the odd one out. 0.03 has a 0 in the tenths column, so it is much smaller.0.03
Check. 0.03 is 3 hundredths, which is not the same as 3 tenths. ✓
Watch out. The 0 after the point matters: 0.03 is not 0.3.
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. Say each number in words and check it against the fraction.
- Look at what Leo wrote. Leo wrote
3 10 3.10 means 3 ones and 10 hundredths (which is 3 and 1 tenth), not 3 tenths. - Find the mistake. Leo wrote the 10 from the bottom of the fraction after the point. The bottom number says that we are counting tenths.
3 10 - Write it correctly. Put the 3 in the tenths column. There are 0 whole ones.
3 10
Check. 0.3 is less than 1 and 3.10 is more than 3, so they cannot be equal. ✓
Watch out. Only the top number goes in the tenths 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. The ones digit is 2 because the number is between 2 and 3. The tenths digit is double the ones digit.
- Find the ones digit. A number between 2 and 3 has 2 ones.ones digit = 2
- Find the tenths digit. It is double the ones digit.2 × 2 = 4
- Write the number. 2 ones and 4 tenths.2.4
Check. 2.4 is between 2 and 3, and the tenths digit 4 is double the ones digit 2. ✓
Watch out. Check every clue in the puzzle at the end.