Year 6 · Decimals
Understand the digits after a decimal point
Learn how to read decimal place value, round decimals, and add, subtract, multiply and divide them, including in real problems.
Definition
A decimal is a number that uses columns smaller than one. The first digit after the decimal point is tenths, the second is hundredths and the third is thousandths, so 0.7 means 710 and 0.35 means 35100. Place value carries straight across the decimal point: each column is worth ten times the column to its right, on both sides of the point. That one fact is behind everything in this unit, from rounding a decimal to dividing one by 1,000.
Why Do I Have to Learn This?
Decimals are how we write amounts between whole numbers, like money and measurements. Prices, heights and race times all use them.
Key Rules:
- 1. The first digit after the decimal point is tenths, the next is hundredths, the next is thousandths, and each column is worth ten times the column to its right.
Remember:
- •Line up the decimal points, and remember each column is worth ten times the one to its right.
Don’t Forget...
- •Lining decimals up from the right-hand end, so 3.7 + 1.25 is set out with the 7 above the 5. The 7 means 7 tenths and the 5 means 5 hundredths, and only digits worth the same can be added. Lining up the decimal points puts 3.70 above 1.25 and gives the correct 4.95.
- •Saying 0.35 is bigger than 0.5 because 35 is bigger than 5. 0.5 is 5 tenths, which is 50 hundredths, while 0.35 is only 35 hundredths. Comparing decimals means comparing place value, not counting digits.
- •Writing 4.5 x 100 as 4.500 by adding zeros on the end. Zeros after the last decimal digit do not change the value: 4.500 is still 4.5. Multiplying by 100 must make every digit worth 100 times more, so the digits move two places left to give 450.
Decimal
A number written with a decimal point.
0.5 is the same as a half.
Worked Example:
Work out 4.36 x 7.
Ignore the decimal point for a moment and multiply the digits: 436 x 7 = 3,052.
4.36 has two digits after the decimal point, so the answer must too: place the point to give 30.52.
Check the size with an estimate: 4.36 is a little more than 4, and 4 x 7 = 28, so 30.52 is sensible.
Answer: 30.52
Why It Works:
Decimal columns follow the same rule as whole-number columns: each one is worth ten times the column to its right. That is why the written column methods work unchanged on decimals, as long as the decimal point keeps every digit in its correct column, and why multiplying by 10 shifts every digit exactly one column to the left.
Another Example:
Six friends share a restaurant bill of £52.20 equally. How much does each friend pay?
Sharing equally means dividing, so work out 52.20 divided by 6.
Divide column by column with the decimal point kept in line: 52 ones divided by 6 is 8, remainder 4.
The remainder 4 carries into the tenths, making 42 tenths: 42 divided by 6 is 7 tenths, and 0 hundredths divided by 6 is 0.
So each friend pays £8.70. Check: £8.70 x 6 = £52.20.
Answer: £8.70 each
Animated Example:
Free Understand the digits after a decimal point Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Before this: Decimals and percentages (Year 5) · Next: Fractions, decimals and percentages (Year 7)
Let’s Practise the Concept
Step 1 of 3
Put the decimals in order
Tap them from smallest to largest.
In order so far: nothing yet