To change a fraction into a decimal, divide the top number (the numerator) by the bottom number (the denominator). For example, 3/4 means 3 ÷ 4, which is 0.75. On a calculator that is all you need to do. Without one, you can use short division or turn the fraction into tenths or hundredths first.
Fractions and decimals appear side by side in almost every free numerical reasoning test, where a table might show one figure as a fraction and ask you to compare it with a decimal or percentage.
How to convert a fraction to a decimal
A fraction is a division waiting to happen. The line between the two numbers means “divided by”.
- Take the numerator. In 3/8, that is 3.
- Divide it by the denominator. 3 ÷ 8 = 0.375.
- Round if the question asks you to. 0.375 to two decimal places is 0.38.
More examples:
- 1/4 = 1 ÷ 4 = 0.25
- 2/5 = 2 ÷ 5 = 0.4
- 7/20 = 7 ÷ 20 = 0.35
- 9/16 = 9 ÷ 16 = 0.5625
How to turn a fraction into a decimal without a calculator
Method 1: make the denominator 10, 100 or 1,000. If you can multiply the bottom number to reach 10, 100 or 1,000, do the same to the top number and read off the decimal.
- 3/5: multiply top and bottom by 2 to get 6/10, which is 0.6.
- 7/25: multiply by 4 to get 28/100, which is 0.28.
- 3/8: multiply by 125 to get 375/1,000, which is 0.375.
This works whenever the denominator is made only of 2s and 5s multiplied together, such as 4, 8, 20, 25, 40 or 50.
Method 2: short division. For any other denominator, divide the numerator by the denominator, adding zeros after a decimal point as you go.
To convert 5/8: 8 does not go into 5, so write 0 and a decimal point, then carry on with 50. 8 goes into 50 six times (48), remainder 2. Then 8 goes into 20 twice (16), remainder 4. Then 8 goes into 40 exactly five times. The answer is 0.625.
Recurring decimals
Some fractions never divide exactly. The digits repeat for ever, and you either round or show the repeat with a dot over the digit.
- 1/3 = 0.333…, usually written 0.33 to two decimal places
- 2/3 = 0.666…, which rounds to 0.67
- 1/6 = 0.1666…, which rounds to 0.17
- 1/7 = 0.142857142857…, where the six digits repeat
You can tell in advance whether a fraction will recur. Simplify it first, then look at the denominator. If its only prime factors are 2 and 5, the decimal stops. If any other prime factor is left, such as 3, 7 or 11, the decimal recurs. So 3/12 stops, because it simplifies to 1/4, but 5/12 recurs, because 12 contains a 3.
Converting mixed numbers and improper fractions
For a mixed number such as 2 3/4, keep the whole number and convert only the fraction: 3/4 = 0.75, so 2 3/4 = 2.75.
For an improper fraction, where the top is bigger than the bottom, divide as normal. 11/4 = 11 ÷ 4 = 2.75, the same value.
Common fractions and their decimals
Knowing these by heart saves time in a test.
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.333… |
| 2/3 | 0.666… |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 5/8 | 0.625 |
| 1/10 | 0.1 |
| 1/20 | 0.05 |
| 1/25 | 0.04 |
Once you have the decimal, the percentage is one step away: multiply by 100, so 3/8 = 0.375 = 37.5%. Our guide to converting fractions, decimals and percentages covers all three directions.
Using fraction to decimal conversions in a test
Converting to a decimal is often the quickest way to find a fraction of an amount or to compare two fractions.
Example 1: a fraction of an amount. A team member works a 37 hour week and spends 3/4 of it on the shop floor. How many hours is that?
3/4 = 0.75, and 37 × 0.75 = 27.75 hours. As hours and minutes, 0.75 of an hour is 45 minutes, so the answer is 27 hours 45 minutes.
Example 2: a discount. A television costing £450 goes on sale at two thirds of its price. How much is saved?
The sale price is 450 × 2 ÷ 3 = £300, so the saving is 450 − 300 = £150. Here it is safer to multiply by 2 and divide by 3 than to use 0.67, because rounding 2/3 to 0.67 would give £301.50.
Example 3: comparing fractions. Region A met 5/8 of its sales target and Region B met 7/11. Which did better?
5/8 = 0.625 and 7/11 = 0.636 (to three decimal places). Region B did slightly better, which is hard to see from the fractions alone.
Ratios behave in a similar way. Once you can write a ratio as a fraction, you can convert it to a decimal the same way. See our guide on how to convert a ratio into a fraction. To go in the opposite direction, read how to write a decimal as a fraction.
When you are confident with the conversions, try them under time pressure in a numerical reasoning test with worked solutions.