Year 6 maths · Key Stage 2 · Number – fractions (including decimals and percentages)

Year 6 fractions, decimals and percentages: converting and rounding

In Year 6 children treat a fraction as a division sum and use it to find decimal equivalents, such as 3/8 = 0.375. They work confidently with numbers up to three decimal places, multiply and divide by 10, 100 and 1,000, multiply and divide decimals by whole numbers, round answers sensibly, and know the common matches between fractions, decimals and percentages.

Decimals, percentages and rounding, explained

A fraction is a division in disguise: 3/8 means 3 ÷ 8. Children use short division to find the decimal, writing 3 as 3.000 and passing each remainder on to the next digit. 3 ÷ 8 = 0.375. Some fractions never end, so 1/3 = 0.333… and 2/3 = 0.666… are recurring decimals. Children round these, so 2/3 is about 0.667 to three decimal places.

Place value goes up to thousandths. In 6.307, the 3 stands for 3 tenths and the 7 for 7 thousandths. Multiplying or dividing by 10, 100 or 1,000 moves every digit one, two or three places left or right, with zeros used as placeholders: 4.56 × 100 = 456, and 83.2 ÷ 100 = 0.832. Many schools teach that the digits move and the decimal point stays where it is, because this works for every number and avoids the “add a zero” trap.

Written calculation extends to decimals. Children multiply a number such as 2.37 by a one-digit whole number (2.37 × 3 = 7.11) using short multiplication and keeping the decimal points in line, often starting with simple cases like 0.4 × 2 = 0.8, and in money and measures such as £1.45 × 6 = £8.70. They also divide using a written method where the answer has up to two decimal places, such as 27 ÷ 4 = 6.75, by continuing the division past the decimal point.

Rounding tells us how precise an answer needs to be. 7.846 is 7.8 to one decimal place and 7.85 to two decimal places. Children round to the nearest whole number, tenth or hundredth as a problem requires, and use rounding to estimate: 4.9 × 6 is roughly 5 × 6 = 30, so an answer of 29.4 is sensible but 2.94 is not. Context matters too. A recipe might be rounded to the nearest 10 g, while a bill must be exact to the penny.

Finally, children are expected to recall the equivalences between simple fractions, decimals and percentages and use them in different contexts. For example: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10% and 1/100 = 0.01 = 1%. A percentage is simply “out of 100”, so 35% is 35/100 = 0.35. Being able to move between the three forms helps with comparing, for instance putting 0.6, 3/5 and 55% in order and noticing that 0.6 and 3/5 are the same amount, both bigger than 55%.

Words your child will hear

Decimal place: A digit after the decimal point. 0.375 has three decimal places.
Tenths, hundredths, thousandths: The first three places after the decimal point, worth 1/10, 1/100 and 1/1,000.
Equivalent: Worth the same amount in a different form, such as 1/4, 0.25 and 25%.
Percentage: A number out of 100, written with the % sign.
Recurring decimal: A decimal whose digits repeat for ever, such as 1/3 = 0.333…
Round: Replace a number with a nearby one that is simpler, such as 2.396 becoming 2.40 to two decimal places.
Degree of accuracy: How exact an answer needs to be, such as nearest whole number or two decimal places.

What the National Curriculum says

In Year 6, pupils should be taught to:

Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8]
Identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places
Multiply one-digit numbers with up to 2 decimal places by whole numbers
Use written division methods in cases where the answer has up to 2 decimal places
Solve problems which require answers to be rounded to specified degrees of accuracy
Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Write 3/8 as a decimal.

A fraction is a division, so 3/8 means 3 ÷ 8. 8 does not go into 3, so write 3 as 3.000, adding zeros after the decimal point. Zeros after the point do not change the value.
Divide with short division. 8 into 3 is 0, remainder 3. Put 0 in the ones place, then the decimal point, and pass the remainder on to make 30.
8 into 30 is 3 (3 × 8 = 24), remainder 6. Write 3 in the tenths place and pass the 6 on to make 60. 8 into 60 is 7 (7 × 8 = 56), remainder 4. Write 7 in the hundredths place and pass the 4 on to make 40.
8 into 40 is exactly 5, with nothing left over, so the division stops. Write 5 in the thousandths place. In your child’s book the remainders 3, 6 and 4 often appear as small digits written just in front of each 0.
```
      0 . 3 7 5
  8 ) 3 . 0 0 0
```
Check by multiplying back: 0.375 × 8 = 3. Or check it by comparison: 3/8 is a little less than 1/2 (0.5), and 0.375 is less than 0.5.

3/8 = 0.375

Common mistakes and how to help

Thinking a decimal with more digits is bigger: 0.45 > 0.7

With whole numbers, 45 is bigger than 7, so a longer number seems larger. The child compares the digits after the point as if they were a whole number.

What helps: Compare place by place from the left, or write both to the same length (0.45 and 0.70). Money helps: 70p is more than 45p. A number line from 0 to 1 also shows it.

Writing 1/4 as 1.4 or 0.4

The child sees the digits in the fraction and puts them either side of a decimal point, without noticing that a fraction is a division.

What helps: Ask for the fraction as a division: 1 ÷ 4. Or use the money link: a quarter of £1 is 25p, which is £0.25. Check that the decimal is sensible: 1/4 must be less than 1/2, which is 0.5.

Believing that × 10 means “add a zero” or that ÷ 10 means “take a zero off”

The shortcut works for whole numbers, so it seems to be the rule. Then 4.5 × 10 becomes 4.50, and 35 ÷ 10 has no zero to take off.

What helps: Show the digits sliding in a place-value grid: every digit moves one column left for × 10 and one column right for ÷ 10. 4.5 × 10 = 45, and 35 ÷ 10 = 3.5.

Cutting off digits instead of rounding: 2.396 to two decimal places is 2.39

The child stops at the second decimal place and ignores the next digit, which says whether to round up.

What helps: Look at the digit one place to the right: 5 or more rounds up. The 6 here sends 2.39 up to 2.40, and the zero stays to show the two decimal places. The same applies to 0.6666… being 0.667.

How to help at home

Money and measures with decimals. Prices, litres and kilograms are decimals in real life. Ask “Six of these at £1.45, how much?” or “What is a quarter of £2.40?” Keep to amounts that your child can work out with a pen, and talk about the estimate first.
Build an equivalence poster. Make a simple chart of the common fractions with their decimals and percentages (1/2, 1/4, 3/4, 1/5, 1/10, 1/100). Put it on the fridge, then quiz each other on a couple of rows at a time.
Calculators for checking only. Ask your child to predict 7 ÷ 8, 5 ÷ 8 and 1 ÷ 6 first, then check. Seeing 0.875 and 0.1666… and rounding them to two or three places builds a feeling for how fractions and decimals relate.
Round it sensibly. In real situations ask what accuracy would be useful: a shopping total to the nearest pound for a quick estimate, a journey to the nearest mile, a cake weight to the nearest 10 g. Linking rounding to a purpose makes the rules easier to remember.
Say the digits and their values. Read a decimal such as 6.307 aloud by place: “six ones, three tenths, no hundredths, seven thousandths.” Then multiply it by 10 and read the new value. The language of place value stays clear.

Updated 20 October 2026.