Common fractions as decimals and percents
| Fraction | Exact decimal | Rounded | Percent |
|---|---|---|---|
| 1/2 | 0.5 | 0.5 | 50% |
| 1/3 | 0.(3) | 0.3333 | 33.3333% |
| 2/3 | 0.(6) | 0.6667 | 66.6667% |
| 1/4 | 0.25 | 0.25 | 25% |
| 3/4 | 0.75 | 0.75 | 75% |
| 1/5 | 0.2 | 0.2 | 20% |
| 2/5 | 0.4 | 0.4 | 40% |
| 3/5 | 0.6 | 0.6 | 60% |
| 4/5 | 0.8 | 0.8 | 80% |
| 1/6 | 0.1(6) | 0.1667 | 16.6667% |
| 5/6 | 0.8(3) | 0.8333 | 83.3333% |
| 1/8 | 0.125 | 0.125 | 12.5% |
| 3/8 | 0.375 | 0.375 | 37.5% |
| 5/8 | 0.625 | 0.625 | 62.5% |
| 7/8 | 0.875 | 0.875 | 87.5% |
| 1/10 | 0.1 | 0.1 | 10% |
| 1/12 | 0.08(3) | 0.0833 | 8.3333% |
| 1/16 | 0.0625 | 0.0625 | 6.25% |
| 3/16 | 0.1875 | 0.1875 | 18.75% |
| 5/16 | 0.3125 | 0.3125 | 31.25% |
| 7/16 | 0.4375 | 0.4375 | 43.75% |
| 9/16 | 0.5625 | 0.5625 | 56.25% |
| 11/16 | 0.6875 | 0.6875 | 68.75% |
| 13/16 | 0.8125 | 0.8125 | 81.25% |
| 15/16 | 0.9375 | 0.9375 | 93.75% |
Brackets mark digits that repeat forever: 0.(3) is 0.333… and 0.1(6) is 0.1666…
How to convert a decimal to a fraction
- Count the decimal places and write the digits over 1 followed by that many zeros: 0.375 → 375/1000.
- Find the greatest common factor of the top and bottom: here 125.
- Divide both by it: 375 ÷ 125 = 3 and 1000 ÷ 125 = 8, so 0.375 = 3/8.
A decimal above 1 works the same way and can then be written as a mixed number: 2.75 = 275/100 = 11/4 = 2 3/4.
Repeating decimals
A repeating decimal is always a fraction too. Take all the digits up to the end of the first repeat, subtract the digits before the repeat, and divide by a number made of one 9 for each repeating digit followed by one 0 for each non-repeating decimal place. For 0.1(6) = 0.1666…: (16 − 1) ÷ 90 = 15/90 = 1/6. The same rule shows that 0.(9), meaning 0.999…, is exactly 1.
Fractions and percents to decimals
To turn a fraction into a decimal, divide the top by the bottom: 5/8 = 5 ÷ 8 = 0.625. A fraction in lowest terms gives a decimal that ends only when its bottom number has no prime factors other than 2 and 5; anything else, like 1/3 or 1/7, repeats forever. A percent is a fraction of 100: 37.5% = 37.5 ÷ 100 = 0.375 = 3/8.
When a decimal is a rounded measurement rather than an exact value, the closest simple fraction is often more useful than the exact one. 3.14159 is exactly 314159/100000, but the closest fraction with a bottom number up to 100 is 311/99. The calculator shows this whenever the exact fraction has a bottom number over 100, and it also gives the nearest sixteenth, the usual step on an inch ruler.
Questions people ask
How do I turn a decimal into a fraction?
Write the digits after the point over 10, 100, 1,000 and so on (one zero per decimal place), then divide the top and bottom by their greatest common factor. 0.375 has three decimal places, so it is 375/1000; both divide by 125, giving 3/8.
How do I enter a repeating decimal like 0.333…?
Put the repeating digits in brackets: 0.(3) for 0.333…, 0.1(6) for 0.1666…, 0.(142857) for 1/7. If you type 0.333 without brackets, the calculator treats it as exactly 333/1000 and also shows the closest simple fraction, 1/3.
How do I turn a fraction into a decimal?
Divide the top number by the bottom number: 5/8 = 5 ÷ 8 = 0.625. Some fractions never end, such as 1/3 = 0.333…; the calculator shows the repeating part in brackets and a rounded value.
How do I convert a decimal or fraction to a percent?
Multiply the decimal by 100: 0.375 × 100 = 37.5%. For a fraction, divide first, then multiply by 100: 3/8 = 0.375 = 37.5%. To go back, divide the percent by 100.
What is a mixed number?
A whole number and a fraction together, such as 2 3/4, which means 2 + 3/4 = 11/4 = 2.75. You can type mixed numbers with a space between the whole number and the fraction.