To write a decimal as a fraction, put the digits after the decimal point over 10, 100 or 1,000, depending on how many decimal places there are, then simplify. For example, 0.75 has two decimal places, so it becomes 75/100, and dividing top and bottom by 25 gives 3/4. One decimal place means tenths, two means hundredths and three means thousandths.
Moving between decimals and fractions is a core skill in any free numerical reasoning test, where a fraction is often the quickest way to work with a figure like 0.125 or 0.6.
How to change a decimal into a fraction
- Count the decimal places. 0.6 has one, 0.45 has two, 0.125 has three.
- Write the digits over the matching power of ten. One place goes over 10, two over 100, three over 1,000.
- Simplify. Divide the top and bottom by their highest common factor.
Worked through:
- 0.6 = 6/10. Divide both by 2 to get 3/5.
- 0.45 = 45/100. Divide both by 5 to get 9/20.
- 0.125 = 125/1,000. Divide both by 125 to get 1/8.
- 0.84 = 84/100. Divide both by 4 to get 21/25.
Why it works: place value
Each position after the decimal point has a value. The first is tenths, the second hundredths and the third thousandths. So 0.37 is 3 tenths and 7 hundredths, which is 37 hundredths, or 37/100. Writing the decimal as a fraction is simply saying out loud what the decimal already means.
Another way to see it is to write the decimal over 1, then multiply top and bottom by 10 until the top is a whole number. 0.45/1 becomes 4.5/10, then 45/100. It is the same answer.
How to simplify the fraction
An unsimplified fraction is still correct, but tests almost always want the simplest form. Find the highest common factor of the top and bottom numbers, the largest number that divides both exactly, and divide by it.
If the highest common factor is not obvious, divide by small numbers in turn. For 0.36 = 36/100, divide by 2 to get 18/50, then by 2 again to get 9/25. Nothing else divides both 9 and 25, so you are finished.
A shortcut: if the bottom is 10, 100 or 1,000, the only numbers that can simplify it are made of 2s and 5s. Try 2, 4, 5, 25 and 125 first.
Decimals greater than 1
Keep the whole number separate and convert only the decimal part.
- 2.4 = 2 and 4/10 = 2 2/5
- 1.35 = 1 and 35/100 = 1 7/20
If you need an improper fraction instead, multiply the whole number by the denominator and add the numerator. 2 2/5 becomes (2 × 5 + 2)/5 = 12/5, and 1 7/20 becomes 27/20.
Recurring decimals
A decimal that repeats for ever, such as 0.333…, cannot be written over a power of ten. A little algebra handles it.
Example: 0.4545…
- Call the number x, so x = 0.4545…
- Two digits repeat, so multiply by 100: 100x = 45.4545…
- Subtract the first line from the second: 99x = 45.
- Divide: x = 45/99, which simplifies to 5/11.
Example: 0.1666…, where only the 6 repeats.
- x = 0.1666…, so 10x = 1.666… and 100x = 16.666…
- Subtract: 100x − 10x = 90x = 15.
- x = 15/90, which simplifies to 1/6.
The two you will meet most often are 0.333… = 1/3 and 0.666… = 2/3. It is worth knowing them on sight.
Common decimals as fractions
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.4 | 2/5 |
| 0.5 | 1/2 |
| 0.6 | 3/5 |
| 0.75 | 3/4 |
| 0.8 | 4/5 |
| 0.125 | 1/8 |
| 0.375 | 3/8 |
| 0.625 | 5/8 |
| 0.875 | 7/8 |
Using decimal to fraction conversions in a test
Fractions make some calculations much easier to do in your head.
Example 1: a share of a workforce. A survey finds that 0.35 of a company’s 240 staff work remotely. How many is that?
0.35 = 35/100 = 7/20. One twentieth of 240 is 12, so 7/20 is 7 × 12 = 84 staff.
Example 2: a rate as “1 in n”. A training course has a failure rate of 0.125. How would you describe that in words?
0.125 = 1/8, so 1 in every 8 candidates fails the course.
Turning a decimal into a fraction is also the first step in writing it as a ratio. A part-to-whole share of 3/8 is a ratio of 3:5 between the two groups. Our guide on how to convert a ratio into a fraction explains how the two link up.
For the opposite direction, see how to convert a fraction to a decimal, and for percentages as well, read our guide to converting fractions, decimals and percentages. Then put the skills to work in a timed numerical reasoning test.