Year 5 maths · Key Stage 2 · Number – fractions (including decimals and percentages)

Year 5 decimals, thousandths and percentages explained

In Year 5 children extend decimals to three places, meeting thousandths for the first time, and learn to read, write, order and round them. They also meet per cent, understanding it as parts per hundred, and learn that fractions, decimals and percentages are three ways of writing the same amount. They learn the key equivalents, such as 1/4 = 0.25 = 25%, and use them to solve problems.

Decimals, thousandths and percentages, explained

Decimals continue the place value pattern into smaller and smaller pieces. In 3.456 the 3 is worth 3 ones, the 4 is worth 4 tenths, the 5 is worth 5 hundredths and the 6 is worth 6 thousandths. Each place is worth one tenth of the place to its left. A thousandth is 1/1,000 and is written 0.001, and children relate it to tenths and hundredths: 0.3 is the same as 3/10, 30/100 and 300/1,000. Measures give the idea something to hold on to, since 1 mm is 0.001 m and 1 g is 0.001 kg.

Children read and write decimals as fractions, so 0.71 = 71/100, 0.7 = 7/10 and 0.307 = 307/1,000. They also compare and order decimals with up to three places by lining up the decimal points and comparing from the left. Writing in the “missing” zeros helps: 0.4, 0.45 and 0.405 become 0.400, 0.450 and 0.405, so the order is 0.4, 0.405, 0.45. Class activities often include counting in steps of 0.1 or 0.01, finding what makes 1 (0.83 + 0.17 = 1), and adding and subtracting tenths in your head.

Rounding means replacing a number with the nearest simpler one. Year 5 children round decimals with two places to the nearest whole number and to one decimal place. To round 7.46 to one decimal place, look at the hundredths digit. It is 6, which is 5 or more, so the tenths digit goes up and 7.46 becomes 7.5. To round to the nearest whole number, look at the tenths digit instead: it is 4, so 7.46 rounds down to 7. A number exactly halfway, such as 3.5, rounds up to 4.

Per cent means “out of 100”, and the % symbol is just a short way to write it. 1% is 1/100 (0.01) and 100% is the whole thing. So 35% is 35/100, which is also 0.35. Children are expected to know the percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5 and 4/5, and of fractions with a denominator that is a multiple of 10 or 25, such as 7/20 = 35/100 = 35%. These are best seen on a hundred square. Finding a percentage of an amount, like 15% of £80, comes later, in Year 6.

Words your child will hear

Decimal point: The dot that separates whole numbers from parts of a whole, as in 3.456.
Tenth: One of 10 equal parts of a whole: 1/10, or 0.1.
Hundredth: One of 100 equal parts of a whole: 1/100, or 0.01.
Thousandth: One of 1,000 equal parts of a whole: 1/1,000, or 0.001.
Decimal place: A digit’s position after the decimal point. 7.46 has two decimal places.
Per cent: Parts per hundred, written %. 40% means 40 out of every 100.
Round: Replace a number with a nearby, simpler one, such as 7.46 to 7.5.

What the National Curriculum says

In Year 5, pupils should be taught to:

Read and write decimal numbers as fractions [for example, 0.71 = 71/100]
Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
Round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
Read, write, order and compare numbers with up to 3 decimal places
Solve problems involving number up to 3 decimal places
Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction
Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25

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

A worked example

Write 2/5 as a percentage and as a decimal.

Per cent means out of 100, so the aim is to write 2/5 as a fraction with 100 on the bottom.
Ask what 5 is multiplied by to make 100: 5 × 20 = 100. Multiply the top by the same number, 2 × 20 = 40, so 2/5 = 40/100.
Forty out of a hundred is 40%.
As a decimal, 40/100 is 40 hundredths, which is 4 tenths and 0 hundredths: 0.40, which is written 0.4.
Check it with a fact your child already knows. 1/5 is 20%, so 2/5 should be double that: 40%.

2/5 = 40/100 = 40% = 0.4

Common mistakes and how to help

Thinking a decimal with more digits is bigger

Children see 0.405 against 0.45 and reason that 405 is bigger than 45. With whole numbers, more digits really does mean a bigger number.

What helps: Compare place by place from the left: both have 4 tenths, but 0.45 has 5 hundredths and 0.405 has none. Writing 0.450 beside 0.405 helps.

Chopping digits off instead of rounding

7.46 becomes 7.4 to one decimal place because the 6 is simply dropped, so the child never checks whether 7.46 is closer to 7.4 or 7.5.

What helps: Draw a number line from 7.4 to 7.5 with the halfway point at 7.45. Where does 7.46 sit? Rounding is choosing the nearer end.

Writing 1/4 as 0.4, or 1/5 as 0.5

The digit in the denominator gets copied after the decimal point, as if 1/4 meant “1 point 4”.

What helps: Convert through hundredths: 1/4 = 25/100 = 0.25. Four quarters make one whole, and 0.4 × 4 is 1.6, so 0.4 can’t be a quarter.

Writing 6% as 0.6

Children drop the % sign and write the number after the point. But 6% is 6 out of 100, which is 6 hundredths: 0.06.

What helps: Read it back as a fraction first, 6/100, then locate the 6 in the hundredths column. Money helps: 6p is £0.06, and it is 6% of £1.

How to help at home

Look for hundredths in money. A penny is 0.01 of a pound. Ask what fraction of £1 and what percentage 45p is (45/100, 45%), then what would be 50% or 25% of £1.
Measure small things. With a ruler, a millimetre is 0.001 of a metre. Ask your child to write the length of a pencil in metres, such as 0.152 m, and say which digit means tenths and which means thousandths.
Spot percentages out and about. Battery levels, sale signs and food labels use percentages. Ask what the sign means as a fraction: 50% off is half price, 25% off is a quarter off, 10% is one tenth.
Make 1 together. Say a decimal such as 0.35 or 0.83 and ask what must be added to reach 1 (0.65 and 0.17). Make it a quick game for car journeys and waiting time.

Updated 20 October 2026.