Fraction to decimal converter
Type a fraction, a mixed number or a decimal. It converts both ways as you type.
Runs in your browser. What you type is not sent to a server.
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as a decimal
- Fraction
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- Mixed number
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- Percent
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Common fractions as decimals
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/6 | 0.1(6) |
| 1/3 | 0.(3) | 1/8 | 0.125 |
| 2/3 | 0.(6) | 3/8 | 0.375 |
| 1/4 | 0.25 | 5/8 | 0.625 |
| 3/4 | 0.75 | 1/9 | 0.(1) |
| 1/5 | 0.2 | 1/16 | 0.0625 |
A part in brackets repeats forever: 0.(3) means 0.333…, and 0.1(6) means 0.1666…. Many books write the same thing with a line over the repeating digits.
How to turn a fraction into a decimal
Divide the top number by the bottom number. For 3/8, 3 ÷ 8 = 0.375. With a mixed number, keep the whole part and convert only the fraction: 2 3/4 is 2 + 0.75 = 2.75. A fraction ends after a few digits only when its bottom number, in lowest terms, has no prime factors other than 2 and 5; that is why 1/8 stops at 0.125 but 1/3 and 1/7 repeat forever.
How to turn a decimal into a fraction
The percent shown next to each result is the decimal times 100, so 3/8 = 0.375 = 37.5%. For percent of a number or percent change, go on to the percentage calculator.
Write the decimal over a power of ten and reduce. 0.625 has three digits after the point, so it is 625/1000, which reduces to 5/8 after dividing both by 125. For a repeating decimal, the converter uses the standard algebra trick: 0.(3) = x, so 10x = 3.(3), and 10x − x = 3, giving x = 1/3. Type the repeating part in brackets, like 0.(3) or 1.2(34), to get the exact fraction instead of a rounded one.
Worked examples
Each row is what the converter shows for that input. The last column is the nearest mark on a ruler or tape measure marked in sixteenths of an inch.
| You type | Fraction | Decimal | Percent | Nearest 1/16 |
|---|---|---|---|---|
| 3/8 | 3/8 | 0.375 | 37.5% | 3/8 |
| 5/12 | 5/12 | 0.41(6) | ≈ 41.67% | 7/16 |
| 1/7 | 1/7 | 0.(142857) | ≈ 14.29% | 1/8 |
| 0.6875 | 11/16 | 0.6875 | 68.75% | 11/16 |
| 0.333 | 333/1000, close to 1/3 | 0.333 | 33.3% | 5/16 |
| 2.3 | 2 3/10 | 2.3 | 230% | 2 5/16 |
| 3.14159 | 3 14159/100000, close to 22/7 | 3.14159 | ≈ 314.16% | 3 1/8 |
1/7 is a good example of how long a repeating block can get: all six digits 142857 repeat, and the converter shows them once in brackets. 5/12 starts with a part that doesn't repeat (41) before the 6 repeats.
Close to and nearest 1/16
A typed decimal like 0.333 is exactly 333/1000, which is correct but rarely what you want. When a simple fraction with a bottom number of 16 or less is within 0.005 of your decimal, the converter adds a Close to line, so 0.333 shows close to 1/3 and 3.14159 shows close to 22/7, the old schoolbook value for pi.
The Nearest 1/16 on a ruler line is for measuring. It rounds to the closest sixteenth and writes anything over 1 as a whole number plus a fraction, the way a tape measure is read: 2.3 inches is about 2 5/16, and 3.14159 is about 3 1/8. A plan that says 0.6875 inches is exactly 11/16.
Questions
How do I find 0.3 inches on a tape measure?
Multiply by 16 and round: 0.3 × 16 = 4.8, which rounds to 5, so look for the 5/16 mark. Type 0.3 above and the nearest 1/16 line does the same sum for you.
Is 0.(9) really equal to 1?
Yes. 1/3 = 0.(3), and three times that is 0.(9) = 3/3 = 1. The converter shows 0.(9) as 1/1.
Why does my calculator show 0.3333333 instead?
Most calculators stop after a fixed number of digits and round the last one. This converter works with whole numbers internally, so it finds the exact repeating pattern instead of rounding.