Decimals and Percentages
In Year 5, decimals stretch to three places, so children read, write, compare and round numbers like 3.482 and recognise thousandths for the first time. The key idea holds it all together: each place is worth ten times the one beside it, so the tenths column counts for far more than the thousandths. None of it is as daunting as it sounds once the decimal point becomes the line everything is measured from.
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
Decimals and percentages
The whole grid is 1 and each square is one hundredth, so 45 shaded squares show 0.45, which is the same as 45%.
For grown-ups
Percentages arrive this year as a new way of writing something children already know. Per cent simply means out of a hundred, so 50% is half, 25% is a quarter, and the same quantity can be written as a fraction, a decimal or a percentage at will. Recalling those few equivalents by heart and using them to find a percentage of an amount is the groundwork for the proportion, ratio and money reasoning that runs right through secondary maths.
What is in this topic
- Thousandths and decimals to three decimal places
- Rounding, comparing and ordering decimals
- Reading scales and number lines with decimals
- The per-cent symbol: percentages as fractions and decimals
- Equivalent fractions, decimals and percentages, and percentage of an amount
- Add and subtract decimals, including making one whole
How to help at home
At this stage decimals and percentages are really one idea seen two ways, so keep the link visible: the same quantity written as a fraction, a decimal and a percentage. Short, frequent practice with real numbers (prices, scores, measurements) does far more than one long sitting.
- Read decimals by place value, not as a long whole number. For 3.482 say 'three point four eight two', then ask which digit is worth the most: the 4 is four tenths (0.4), the 8 is eight hundredths (0.08) and the 2 is two thousandths (0.002), so 0.4 is the biggest because each place is worth ten times the one to its right.
- Pin down the three or four equivalents that unlock the rest. Drill that 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25% and 3/4 = 0.75 = 75%, then ask for one of the three at random until any one springs the other two.
- Find a percentage by building on 10%. To get 10% just divide by 10, so 10% of 80 is 8, then 5% is half of that (4), so 15% of 80 is 8 + 4 = 12.
- Round decimals by looking only at the next digit along. To round 3.466 to two decimal places, the third digit is 6, so it rounds up to 3.47; to one place the second digit is 6, so it becomes 3.5.
Where children get stuck
The commonest slip is judging a decimal by how many digits it has, so a child reads 0.45 as larger than 0.5 because it 'has more numbers'. The fix is to line the numbers up by the point and compare one place at a time: 0.5 is five tenths, 0.45 is only four tenths and a bit, so 0.5 wins. Writing 0.5 as 0.50 so both have the same number of places makes the comparison obvious.
The other regular wobble is muddling what a percentage is out of. Children find 10% of a number but then think 25% must be 'a quarter of that 10%', or they treat 50% as 50 rather than half. Anchor it with 'per cent means out of 100, so 50% is 50 out of every 100, which is just half', and check against the equivalents: 25% is a quarter, so 25% of 80 is 80 / 4 = 20.