To convert between fractions, decimals and percentages, divide the top of a fraction by the bottom to get a decimal, then multiply the decimal by 100 to get a percentage.
Every other conversion is one of those two moves run backwards. The three forms are simply different ways of writing the same proportion: one half, 0.5 and 50% are the same amount. This guide shows each conversion with worked examples, the equivalents that save time when you know them by heart, how to deal with recurring decimals, and what the national curriculum and the GCSE ask for.
What fractions, decimals and percentages have in common
A fraction, a decimal and a percentage all describe a part of a whole. The fraction says it with a top and a bottom number, the decimal with place value, and the percentage as a number of parts out of 100. That last idea is the key to most conversions: per cent means per hundred, so 35% is 35 out of 100.
Because the three forms are interchangeable, you can pick whichever makes the calculation easier. Comparing 3/5, 0.58 and 61% is hard as written; turned into decimals they become 0.6, 0.58 and 0.61, and the order is obvious: 0.58, then 0.6, then 0.61.
The table below sums up the six possible conversions. The rest of the guide takes them one at a time.
| From | To | How | Example |
|---|---|---|---|
| Fraction | Decimal | Divide top by bottom | 3/8 = 3 ÷ 8 = 0.375 |
| Decimal | Percentage | Multiply by 100 | 0.375 × 100 = 37.5% |
| Percentage | Decimal | Divide by 100 | 12% = 0.12 |
| Percentage | Fraction | Write over 100, simplify | 35% = 35/100 = 7/20 |
| Decimal | Fraction | Use place value, simplify | 0.45 = 45/100 = 9/20 |
| Fraction | Percentage | Make the bottom 100 | 7/25 = 28/100 = 28% |
Fraction to decimal: divide the top by the bottom
A fraction is a division waiting to happen: 3/8 means 3 ÷ 8. Doing that division gives the decimal. 3 ÷ 8 is 0.375, which you can find by short division or by halving: 1/2 is 0.5, 1/4 is 0.25, 1/8 is 0.125, and three of those make 0.375.
When the bottom number divides into 10, 100 or 1,000, there is a quicker route. Scale the fraction so the bottom becomes one of those, then read the decimal off:
- 3/5 = 6/10 = 0.6
- 7/20 = 35/100 = 0.35
- 9/25 = 36/100 = 0.36
- 13/50 = 26/100 = 0.26
Some fractions never end. 1/3 gives 0.333..., with the 3 repeating forever; this is a recurring decimal, written with a dot over the repeating digit. Any fraction whose bottom number, once simplified, has a prime factor other than 2 or 5 gives a recurring decimal: thirds, sixths, sevenths and ninths all do.
Decimal to percentage, and back
To turn a decimal into a percentage, multiply by 100, which moves every digit two places to the left on the place value chart. 0.35 becomes 35%, 0.07 becomes 7%, and 1.2 becomes 120%. A percentage above 100 just means more than the whole.
Going back, divide by 100: 64% is 0.64, 5% is 0.05, and 12.5% is 0.125. The most common slip is with single digits: 5% is 0.05, not 0.5, because it is 5 hundredths.
This decimal form is the one to use in money questions. A 15% increase means multiplying by 1.15, and a 15% discount means multiplying by 0.85; our guide to percentages in your head uses the same multipliers for quick mental work.
Percentage to fraction, then simplify
A percentage is already a fraction over 100, so write it that way and simplify by dividing top and bottom by the same number:
- 35% = 35/100 = 7/20 (divide both by 5)
- 48% = 48/100 = 12/25 (divide both by 4)
- 75% = 75/100 = 3/4 (divide both by 25)
Decimals follow the same pattern through place value. 0.45 is 45 hundredths, so 45/100, which simplifies to 9/20. 0.375 is 375 thousandths, 375/1,000, which simplifies to 3/8 once you divide by 125.
Percentages with a decimal part need one extra step: 12.5% is 12.5/100, and doubling top and bottom gives 25/200, which is 1/8.
Equivalent fractions, decimals and percentages to know by heart
A small set of equivalents comes up again and again, in shops, in news reports and in exam questions. Knowing them by heart saves a division every time.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/20 | 0.05 | 5% |
| 1/3 | 0.333... | 33.3% (rounded) |
| 2/3 | 0.666... | 66.7% (rounded) |
Equivalent fractions extend the list for free. 2/4, 3/6 and 50/100 are all the same as 1/2, so they are all 0.5 and 50%. Whenever a fraction is not in the table, simplify it first: 6/8 becomes 3/4, which you already know is 0.75.
Recurring decimals back to fractions
Turning a recurring decimal into a fraction uses a neat trick. Take 0.272727..., where 27 repeats. Call it x. Multiply by 100, because two digits repeat: 100x = 27.2727... Subtract the first line from the second and the repeating part disappears: 99x = 27, so x = 27/99, which simplifies to 3/11.
With one repeating digit, multiply by 10 instead: 0.444... gives 10x = 4.444..., so 9x = 4 and x = 4/9. This method belongs to the Higher tier of the GCSE; at Foundation, recognising 0.333... as 1/3 and 0.666... as 2/3 is usually what is needed.
What Year 6 and GCSE expect
The national curriculum in England builds this up over two years of primary school. In Year 5, pupils learn that per cent relates to the number of parts per 100 and write percentages as a fraction with denominator 100 and as a decimal, with the equivalents of 1/2, 1/4, 1/5, 2/5 and 4/5. In Year 6, they associate a fraction with division, calculate decimal equivalents such as 0.375 for 3/8, and recall and use equivalences between simple fractions, decimals and percentages. Questions on these equivalences can come up in the papers described in our guide to the Year 6 maths SATs.
At GCSE, the AQA specification asks students to work interchangeably with terminating decimals and their corresponding fractions, giving 0.375 and 3/8 as an example, and to interpret percentages and percentage changes as a fraction or a decimal. Changing recurring decimals into fractions, and back, is Higher tier content.
These conversions are worth knowing without a calculator, which is why the equivalents table is worth learning by heart; our guide to the non-calculator GCSE maths paper has more on that paper.
Practise the conversions in your head
Speed comes from a few short drills rather than long sessions:
- Say the decimal and the percentage for each fraction in the table, then cover the table and test yourself the next day.
- Pick prices in a shop and work out 10%, 20% and 25% of them.
- Order three mixed values, such as 2/3, 0.7 and 65%, by turning them all into decimals first.
Each drill takes a couple of minutes, and the facts stick when you come back to them a few days later. Kalc trains times tables, fractions, percentages and algebra in about ten minutes a day.
Frequently asked questions
How do you turn a fraction into a decimal?
Divide the top number by the bottom number. 3/8 is 3 divided by 8, which is 0.375. If the bottom number divides into 10 or 100, scale the fraction first: 7/20 is 35/100, which is 0.35.
How do you change a decimal into a percentage?
Multiply by 100. 0.35 becomes 35%, 0.07 becomes 7% and 1.2 becomes 120%.
How do you write a percentage as a fraction?
Put it over 100 and simplify. 35% is 35/100, which simplifies to 7/20.
What is 1/3 as a decimal and a percentage?
1/3 is the recurring decimal 0.333..., about 33.3% when rounded to one decimal place.
When do pupils learn fractions, decimals and percentages in England?
The national curriculum introduces percentages in Year 5 and asks pupils to recall equivalences between simple fractions, decimals and percentages in Year 6. The GCSE builds on this, with recurring decimals at Higher tier.
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