Ross MackellUK-qualified primary teacher · 9 min read

Which is bigger: 35, 0.55 or 58%? Most adults hesitate. Lots of children guess 58%, because 58 looks like the biggest number. The answer is 35, which is 60%.

Fractions, decimals and percentages look like three different topics, and that's exactly why children find them confusing. The truth is they're three ways of writing the same amount, and once your child sees that, the conversions stop feeling like magic tricks.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll show you the one idea that links them, the equivalents worth knowing by heart, how to convert in every direction, how to put a mixed list in order, the mistakes I see most often, and practice questions with answers.

What your child needs first

Converting between fractions, decimals and percentages draws on three skills your child may have learned separately:

• Decimal place value. Knowing that in 0.45 the 4 is worth 4 tenths and the 5 is worth 5 hundredths. If that's wobbly, start with what is place value.
• Equivalent fractions. Turning 320 into 15100, and simplifying 35100 to 720. Here's my guide to equivalent fractions and simplifying.
• Multiplying and dividing by 100. Every decimal and percentage conversion uses it. See multiplying and dividing by 10, 100 and 1000.

In the national curriculum, children write tenths and hundredths as decimals in Year 4, meet percentages and the key equivalents in Year 5, and by Year 6 they're expected to recall and use equivalences between simple fractions, decimals and percentages, including working out decimals like 0.375 for fractions like 3/8.

The one idea that links them

Here's a bar showing one whole, split into four equal parts. Three of the parts are shaded.

Now imagine the same bar split into 100 tiny parts instead. 75 of them would be shaded. That's why 75% (75 out of 100) and 0.75 (75 hundredths) and three quarters are all the same thing.

The equivalents worth knowing by heart

You don't need to work these out every time. Children who just know them find SATs questions on percentages, fractions of amounts and ordering much quicker. These are the ones I'd learn first:

A nice trick for learning them: start with 12 = 50% and 110 = 10%, then build the rest. 14 is half of a half, so it's half of 50%: 25%. 15 is double 110: 20%. 18 is half of 14: 12.5%.

Converting to a percentage

Example 1: fraction to percentage, 320

1. Ask: what do I multiply 20 by to get 100? 20 × 5 = 100.
2. Do the same to the top: 3 × 5 = 15. So 320 = 15100.
3. 15 out of 100 is 15%.

This works whenever the bottom number goes into 100: halves, quarters, fifths, tenths, twentieths, twenty-fifths and fiftieths. For 725: 25 × 4 = 100, and 7 × 4 = 28, so it's 28%.

Example 2: decimal to percentage, 0.35 and 0.4

Multiply by 100. The digits move two places to the left.

• 0.35 × 100 = 35, so 0.35 = 35%.
• 0.4 × 100 = 40, so 0.4 = 40%. (Not 4%! More on this in the mistakes section.)
• 0.125 × 100 = 12.5, so 0.125 = 12.5%.

Example 3: fraction to decimal, 38

8 doesn't go into 100 neatly, so use the other big idea: a fraction is a division. 38 means 3 ÷ 8.

1. Write 3 as 3.000 so there's room to divide (adding zeros after the decimal point doesn't change its value).
2. Use the bus stop method: 3 ÷ 8 = 0.375.
3. So 38 = 0.375, which is 37.5%.

This is a classic Year 6 question, and it's exactly the example the national curriculum uses.

Converting from a percentage

Example 4: percentage to decimal, 65% and 5%

Divide by 100. The digits move two places to the right.

• 65% ÷ 100 = 0.65.
• 5% ÷ 100 = 0.05. (Not 0.5! 0.5 is 50%.)

Example 5: percentage to fraction, 35% and 80%

Write the percentage as a fraction out of 100, then simplify.

• 35% = 35100. Both numbers are in the 5 times table, so divide by 5: 720.
• 80% = 80100. Divide both by 20: 45.

If simplifying is the sticking point, it's worth revisiting equivalent fractions before going further.

Decimals to fractions (and back)

Example 6: decimal to fraction, 0.6, 0.45 and 0.125

Read the decimal out loud using place value, and the fraction writes itself.

• 0.6 is "6 tenths" = 610 = 35.
• 0.45 is "45 hundredths" = 45100 = 920.
• 0.125 is "125 thousandths" = 1251000 = 18.

The number of decimal places tells you the bottom number: one place means tenths, two places means hundredths, three places means thousandths. For fraction to decimal, go the other way: get the bottom number to 10, 100 or 1000, or divide the top by the bottom as in Example 3.

Putting a mixed list in order

This is the most common way these skills get tested: a list with a mix of fractions, decimals and percentages, to put in order. The trick is to convert everything into the same form first. I always use percentages, because children find whole numbers easiest to compare.

Example 7: order 0.7, 34, 68%, 0.07

Smallest to largest: 7%, 68%, 70%, 75%. So the answer is 0.07, 68%, 0.7, 34. Remember to write the answer using the original numbers, not your converted ones.

4 common mistakes and how to fix them

Mistake 1: 0.4 = 4%

This is the most common one by far. Your child sees the 4 and writes 4%.

The fix: 0.4 is 4 tenths, and 4 tenths is the same as 40 hundredths. Or simply: multiply by 100, which moves the 4 two places to 40. A quick sense check helps too: 0.4 is nearly a half, and 4% is tiny.

Mistake 2: 14 = 0.4

Children copy the digit from the bottom of the fraction into the decimal. The same mistake gives 15 = 0.5.

The fix: ask "is a quarter bigger or smaller than a half?" Smaller. Is 0.4 smaller than 0.5? Barely. A quarter is half of a half: 0.25. Learning the equivalents table above stops this mistake for good.

Mistake 3: Mixing up 0.7 and 0.07

When ordering, children see 0.07 and 0.7 and think they're nearly the same, or that 0.07 is bigger because it "has more digits".

The fix: convert both to percentages: 70% and 7%. The difference is suddenly obvious. If this keeps happening, decimal place value needs some attention.

Mistake 4: 13 = 0.3 or 30%

13 is 0.333..., with the 3s going on forever. It's roughly 33.3%, not 30%.

The fix: three thirds make a whole, so three lots of 30% would only make 90%. That's a nice one to talk through, because it shows your child how to check an answer for themselves.

Practice questions

Same three steps I use for every skill: watch, copy, practise. Do the first one out loud yourself, then let your child have a go at a similar one before they try the rest on their own. Cover the last two columns and ask your child to fill in the gaps.

Bonus ordering question: put 0.6, 58, 58% and 0.065 in order from smallest to largest. (Answer: 0.065, 58%, 0.6, 58, because they're 6.5%, 58%, 60% and 62.5%.)

Ten minutes, a few times a week, is plenty. Only move on when they're getting three in a row right.

Frequently asked questions

How do you convert a fraction to a percentage?

Make the bottom number (denominator) 100 by multiplying the top and bottom by the same number. The top number is then the percentage. For example, 3/20: multiply top and bottom by 5 to get 15/100, which is 15%. If the denominator doesn't go into 100, divide the top by the bottom to get a decimal, then multiply by 100.

How do you turn a decimal into a percentage?

Multiply the decimal by 100. For example, 0.35 × 100 = 35, so 0.35 = 35%. Be careful with one decimal place: 0.4 is 40%, not 4%.

How do you turn a percentage into a fraction?

Write the percentage as a fraction out of 100, then simplify it. For example, 35% = 35/100, and dividing the top and bottom by 5 gives 7/20.

What year do children learn fractions, decimals and percentages?

In England, children write tenths and hundredths as decimals in Year 4, and are introduced to percentages in Year 5, where they learn the percentage and decimal equivalents of fractions like 1/2, 1/4, 1/5, 2/5 and 4/5. In Year 6 they recall and use equivalences between simple fractions, decimals and percentages, and calculate decimal equivalents such as 0.375 for 3/8.

What is 1/8 as a decimal and a percentage?

1/8 is 0.125 as a decimal and 12.5% as a percentage. An easy way to remember it: 1/4 is 25%, and 1/8 is half of a quarter, so it's half of 25%, which is 12.5%.

Sources and further reading

• Department for Education, National curriculum in England: mathematics programmes of study (fractions, including decimals and percentages, Years 4 to 6)
• Standards and Testing Agency, Key stage 2 mathematics test framework
• Ross Mackell, Teacher's Perspective on YouTube