Everyday · 3 min read
How to Convert Fractions, Decimals and Percentages
Fractions, decimals and percentages are three ways of writing the same thing. Converting between them comes down to three moves: divide to turn a fraction into a decimal, multiply by 100 to turn a decimal into a percentage, and write over a power of ten and simplify to turn a decimal back into a fraction.
Fraction → decimal: divide the top by the bottom
- 3/4 = 3 ÷ 4 = 0.75
- 5/8 = 5 ÷ 8 = 0.625
- 2/3 = 2 ÷ 3 = 0.666… (the 6 repeats forever)
If the denominator only has 2s and 5s as factors (2, 4, 5, 8, 10, 20, 25…), the decimal ends. Anything else, like 3, 6, 7, 9 or 11, gives a repeating decimal.
Decimal → percentage: multiply by 100
- 0.75 → 75%
- 0.625 → 62.5%
- 0.05 → 5% (a common slip is writing 50%)
- 1.2 → 120%
Going the other way, divide by 100: 37.5% = 0.375.
Decimal → fraction: use place value
- Count the digits after the decimal point. That tells you whether it's tenths, hundredths or thousandths.
- Write the digits over 10, 100 or 1,000.
- Simplify.
0.45 = 45/100 = 9/20 (divide both by 5).
0.375 = 375/1000 = 3/8 (divide both by 125).
2.6 = 2 6/10 = 2 3/5.
The "decimal to fraction" box in the fraction calculator does this instantly.
Percentage → fraction
Write the percentage over 100 and simplify. 12.5% = 12.5/100 = 125/1000 = 1/8. 80% = 80/100 = 4/5.
Repeating decimals back to fractions
A handy trick for simple repeats: a single repeating digit is that digit over 9. So 0.333… = 3/9 = 1/3, and 0.777… = 7/9. Two repeating digits go over 99: 0.272727… = 27/99 = 3/11. If the repeat starts later, as in 0.1666…, it's easiest to recognise it: 0.1666… is 1/6.
Cheat sheet
| Fraction | Decimal | Percent |
|---|---|---|
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/6 | 0.1666… | 16.7% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.3% |
| 3/8 | 0.375 | 37.5% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.666… | 66.7% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
Where this comes up
- Test scores: 34 out of 40 is 34/40 = 0.85 = 85%. The grade calculator handles weighted versions.
- Discounts: "a third off" is about 33.3%, so a $60 item becomes $40.
- Recipes and DIY: 0.625 inches is 5/8".
- Money: interest rates and tax rates are percentages that you'll often need as decimals for a formula (5% = 0.05).
For percentage questions like "what percent is X of Y" or percentage increase, the percentage calculator is quicker still.
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example 3/8 = 3 ÷ 8 = 0.375.
How do you convert a decimal to a fraction?
Write the decimal digits over 10, 100 or 1,000 depending on the number of decimal places, then simplify. 0.45 = 45/100 = 9/20.
How do you convert a decimal to a percentage?
Multiply by 100. 0.625 becomes 62.5%.
What is 1/3 as a percentage?
About 33.3%. As a decimal it's 0.333…, with the 3 repeating.