To convert a percentage to a fraction, write it over 100 and simplify. To convert a percentage to a decimal, divide it by 100. To go the other way, divide the top of a fraction by the bottom to get a decimal, then multiply the decimal by 100 to get a percentage. So 22.5% is 22.5 ÷ 100 = 0.225 as a decimal, and 225/1000 = 9/40 as a fraction.
These conversions turn up inside almost every free numerical reasoning test, often without a calculator, so it pays to be quick at all six directions.
The conversions at a glance
| To convert | Do this | Example |
|---|---|---|
| Percentage to decimal | Divide by 100 | 45% = 0.45 |
| Percentage to fraction | Write over 100, then simplify | 45% = 45/100 = 9/20 |
| Decimal to percentage | Multiply by 100 | 0.45 = 45% |
| Decimal to fraction | Write over 10, 100 or 1000, then simplify | 0.45 = 45/100 = 9/20 |
| Fraction to decimal | Divide the top by the bottom | 9/20 = 9 ÷ 20 = 0.45 |
| Fraction to percentage | Divide, then multiply by 100 | 9/20 = 0.45 = 45% |
The top number of a fraction is the numerator and the bottom number is the denominator.
How to convert a percentage to a fraction
Per cent means “per hundred”, so every percentage is already a fraction out of 100.
- Write the percentage over 100. 22.5% becomes 22.5/100.
- Make the numerator a whole number. Multiply the top and bottom by 10 for each digit after the decimal point. 22.5/100 becomes 225/1000.
- Simplify. Divide the top and bottom by the largest number that goes into both. For 225 and 1000 that is 25, giving 9/40.
- Turn an improper fraction into a mixed number if needed. This only happens for percentages above 100.
If you cannot see the largest common factor straight away, divide by small primes in turn: 2, then 3, then 5, then 7. For 225/1000, dividing by 5 gives 45/200, and dividing by 5 again gives 9/40. Nine and 40 share no other factor, so 9/40 is fully simplified.
More examples:
- 32% = 32/100. Both divide by 4, giving 8/25.
- 55% = 55/100. Both divide by 5, giving 11/20.
- 250% = 250/100. Both divide by 50, giving 5/2, which is 2 1/2 as a mixed number.
How to convert a percentage to a decimal
Divide by 100, which moves the decimal point two places to the left.
- 45% = 0.45
- 7.5% = 0.075
- 120% = 1.2
A common slip is writing 7.5% as 0.75. Moving two places from 7.5 gives 0.075. If in doubt, check that 0.075 × 100 gets you back to 7.5.
How to turn a fraction into a decimal and a percentage
Divide the numerator by the denominator to get the decimal, then multiply by 100 for the percentage.
3/8: 3 ÷ 8 = 0.375, and 0.375 × 100 = 37.5%.
If the denominator divides neatly into 100, there is a quicker route. Scale the fraction up so the denominator becomes 100 and read off the percentage.
11/20: 20 goes into 100 five times, so multiply top and bottom by 5 to get 55/100. That is 0.55, or 55%.
Some fractions give a recurring decimal. 1/3 = 0.333… which is 33.3% to one decimal place, and 2/3 = 0.666… which rounds to 66.7%. In a test, round only at the end so the error does not grow. Our guide on how to convert a fraction to a decimal covers long division for awkward denominators.
How to convert a decimal to a fraction and a percentage
Multiply by 100 for the percentage. For the fraction, write the digits over 10, 100 or 1000, depending on how many decimal places there are, and simplify.
- 0.65 = 65%. As a fraction, 65/100, and both divide by 5, giving 13/20.
- 0.125 = 12.5%. As a fraction, 125/1000, and both divide by 125, giving 1/8.
There is more on this direction in our guide on how to write a decimal as a fraction.
Worked example: a workplace question
Test questions rarely ask for a conversion on its own. More often the figures arrive in different forms and you have to put them on the same footing.
Question: A team has 40 staff. Three eighths work fully remotely and 0.45 of the team work hybrid. The rest are based in the office. What percentage of the team is office based, and how many people is that?
- Convert everything to percentages. 3/8 = 0.375 = 37.5%. 0.45 = 45%.
- Add them: 37.5% + 45% = 82.5%.
- Subtract from 100%: 100% minus 82.5% leaves 17.5% in the office.
- Find 17.5% of 40: 40 × 0.175 = 7 people.
Check: 3/8 of 40 is 15 people and 0.45 of 40 is 18 people. 15 + 18 = 33, and 40 minus 33 is 7.
Once percentages are second nature, the next step is percentage change. Our guide on how to calculate percentage increase builds directly on this.
Conversions worth memorising
Knowing these on sight saves time, because you can write the answer down without working it through.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 2/3 | 0.666… | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
| 9/40 | 0.225 | 22.5% |
Practise the conversions under time pressure
Knowing the method is the first step. Being fast enough to use it in a timed assessment comes from practice. Try a free numerical reasoning test and note any question where a conversion slowed you down.
