Decimals and Percentages
By Year 6, children handle decimals with real confidence, working with numbers to three places and saying exactly what each digit is worth. They multiply and divide by 10, 100 and 1000, multiply a decimal by a whole number, and carry out written division that gives a decimal answer. Alongside this they round to a sensible degree of accuracy and start to see fractions, decimals and percentages as three faces of the same amount.
Practise Decimals and Percentages
Have a guess, even if you're not sure. Get one wrong and we'll show you why, so every miss is a chance to learn.
Timed practice
The same practice, just with a gentle clock. Pick a length and see how many you can answer.
Good to know
One whole, split into hundredths
Each square is one hundredth of the whole grid, so 60 shaded squares show 0.6, which is 60% and the same as three fifths.
For grown-ups
The heart of this topic is moving freely between fractions, decimals and percentages, because a fraction is really just a division: three-quarters means 3 divided by 4, which is 0.75, which is 75%. Children turn a fraction into its decimal, switch between all three forms, find a percentage of an amount, and work out a percentage change. This fluency is what makes proportion, ratio and the everyday percentages of secondary maths feel familiar rather than new, so the more comfortable it becomes now, the more it pays off later.
What is in this topic
- Decimals to three places: place value, and multiplying and dividing by 10, 100 and 1000
- Multiplying a decimal by a whole number, and written division with a decimal answer
- Turning a fraction into a decimal, and rounding to a degree of accuracy
- Matching equivalent fractions, decimals and percentages
- Finding a percentage of an amount
- Percentage problems, including percentage change
How to help at home
Decimals and percentages reward little-and-often practice over one big push. The aim is for your child to see fractions, decimals and percentages as three faces of the same amount, so a few focused minutes a day, kept light, builds far more fluency than a long weekend session.
- Practise multiplying and dividing by 10, 100 and 1000 as the digits sliding along the place-value columns, not as adding zeros. Say it aloud: 4.7 multiplied by 100 means each digit moves two places left, so 4.7 becomes 470.
- Turn one fraction into all three forms together, since they are the same amount written differently. Take three-quarters: 3 divided by 4 is 0.75, and 0.75 is 75 hundredths, which is 75%. Repeat with a half (0.5 and 50%) and a fifth (0.2 and 20%).
- Find a percentage by building it from 10%. To get 30% of 250, first find 10% by dividing by 10 to get 25, then multiply by 3 to reach 75. Finding 10% first turns an awkward sum into an easy one.
- Check decimal answers by reading the place value out loud. For 0.6, say 'six tenths', so it is 60% and bigger than 0.45, which is 'forty-five hundredths'. Naming the columns stops the longer-looking number being read as the larger one.
Where children get stuck
The most common slip is treating a decimal as a percentage by just removing the dot, so 0.6 gets read as 6% instead of 60%. The fix is to anchor on the whole: 0.6 is six tenths, the same as sixty hundredths, and a percentage is always out of a hundred, so 0.6 equals 60%. Practise both directions, 0.6 to 60% and back, until reading it as sixty out of a hundred feels automatic.
The other frequent wobble is comparing decimals by length and deciding 0.45 is bigger than 0.6 because it has more digits. Line the numbers up by their decimal points and compare column by column, tenths first: 0.6 has six tenths while 0.45 has only four, so 0.6 wins. Writing the missing zero as 0.60 makes the comparison plain.