Year 6 · Mathematics
Decimals for Year 6: place value, adding and multiplying by 10, 100 and 1000
Decimals are a way of writing numbers that include parts of a whole. Each place to the right of the decimal point is ten times smaller than the place before it.
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Try asking: “How do I multiply decimals by 10?”
Decimal place value
In 4.326, the 3 means 3 tenths, the 2 means 2 hundredths and the 6 means 6 thousandths.
- 0.1 is one tenth (1/10)
- 0.01 is one hundredth (1/100)
- 0.001 is one thousandth (1/1000)
Adding and subtracting decimals
Line up the decimal points so that tenths are under tenths and hundredths are under hundredths. If the numbers have a different number of decimal places, you can write zeros on the end — 2.5 is the same as 2.50.
Multiplying and dividing by 10, 100 and 1000
Multiplying by 10 makes every digit worth ten times as much, so each digit moves one place to the left. Multiplying by 100 moves digits two places, and by 1000 three places. Dividing moves the digits to the right.
It can look like the decimal point is moving, but really the digits are moving between place-value columns.
Decimals and fractions
0.75 means 75 hundredths, which is 75/100. Simplifying gives 3/4.
Worked examples
What is 3.6 + 2.45?
- Write 3.6 as 3.60 so both numbers have two decimal places.
- Add hundredths: 0 + 5 = 5. Tenths: 6 + 4 = 10, write 0 and carry 1. Ones: 3 + 2 + 1 = 6.
Answer: 6.05
What is 4.27 × 100?
- Multiplying by 100 moves each digit two places to the left.
- The 4 ones become 4 hundreds, the 2 tenths become 2 tens, and the 7 hundredths become 7 ones.
Answer: 427
Write 0.4 as a fraction in simplest form.
- 0.4 is 4 tenths: 4/10.
- Divide the numerator and denominator by 2.
Answer: 2/5
Common mistakes to watch for
- Lining up the last digits instead of the decimal points.
- Thinking 0.45 is bigger than 0.5 because 45 is bigger than 5.
- 'Adding a zero' when multiplying a decimal by 10 (3.2 × 10 is 32, not 3.20).
Practice questions
Try these, then reveal the answers. For more questions with hints, use the tutor.
1. What is 5.3 + 1.28?
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6.58
2. What is 7.5 − 2.25?
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5.25
3. What is 0.36 × 10?
Show answer
3.6
4. What is 52 ÷ 1000?
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0.052
5. Write 0.25 as a fraction in simplest form.
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1/4