Fraction to Decimal Calculator
Turn a fraction or mixed number into a decimal and a percent. Find out whether the decimal ends or repeats, then watch the long division digit by digit.
For a repeating decimal, type the digits that repeat in their own box, or write 0.1666… or 0.1(6).
As a fraction
3/4
0.75 = 3/4 as a fraction, or 75% as a percent.
- Fraction
- 3/4
- Decimal
- 0.75
- Percent
- 75%
Show me how
Why does this work?
All steps as text
Tip: press ← and → to move between steps, or click any step.
How to convert a fraction to a decimal
A fraction is a division: divide the top number by the bottom number. 3/8 = 3 ÷ 8 = 0.375. With long division:
- 8 doesn’t go into 3, so write 0 and a decimal point, add a 0 to the 3 and divide 30 by 8: 3, remainder 6.
- Bring down another 0: 60 ÷ 8 = 7, remainder 4.
- Bring down another 0: 40 ÷ 8 = 5, remainder 0. The division ends, and 3/8 = 0.375.
For a mixed number, convert the fraction and put the whole number in front: 2 3/8 = 2 + 0.375 = 2.375.
Will the decimal end or repeat?
Simplify the fraction, then look at the prime factors of the bottom number:
- Only 2s and 5s: the decimal ends. 3/8 = 0.375 (8 = 2 × 2 × 2) and 7/20 = 0.35 (20 = 2 × 2 × 5).
- Any other prime factor: the decimal repeats forever. 1/3 = 0.333…, 5/6 = 0.8333… and 1/7 = 0.142857142857…
The repeating block is always shorter than the bottom number: dividing by 7 leaves remainders from 1 to 6, so after at most 6 digits a remainder comes back and the digits start again. 1/7 repeats 6 digits and 1/17 repeats 16.
Shortcut: make the bottom 10, 100 or 1000
When the bottom number divides a power of 10, multiply the top and the bottom by the same number to get there: 3/8 = 375/1000 = 0.375 (× 125), 7/20 = 35/100 = 0.35 (× 5), and 3/25 = 12/100 = 0.12 (× 4).
Writing repeating decimals
0.1666…, where the 6 repeats, can be written with a bar over the repeating digit, 0.16, with dots, or with brackets, 0.1(6). Calculators run out of digits and round: 1/6 shows as 0.1666666667. To round it yourself, look at the next digit: 2/3 = 0.6666… is 0.67 to two decimal places.
Common fractions as decimals and percents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33 1/3% |
| 2/3 | 0.666… | 66 2/3% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/6 | 0.1666… | 16 2/3% |
| 5/6 | 0.8333… | 83 1/3% |
| 1/7 | 0.142857… | 14 2/7% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/9 | 0.111… | 11 1/9% |
| 1/10 | 0.1 | 10% |
| 1/11 | 0.0909… | 9 1/11% |
| 1/12 | 0.08333… | 8 1/3% |
| 1/16 | 0.0625 | 6.25% |
| 1/20 | 0.05 | 5% |
| 1/25 | 0.04 | 4% |
| 1/100 | 0.01 | 1% |
Questions
How do you convert a fraction to a decimal?
Divide the top number by the bottom number, with long division or a calculator: 5/8 = 5 ÷ 8 = 0.625.
What is 1/3 as a decimal?
0.333…, with the 3 repeating forever. Rounded, it is 0.33 to two decimal places or 0.333 to three.
How do I convert a mixed number to a decimal?
Convert the fraction part and add the whole number: 2 3/4 = 2 + 0.75 = 2.75. Or make it an improper fraction first: 11/4 = 11 ÷ 4 = 2.75.
Why does 1/7 repeat six digits?
In long division by 7, the remainder is always 1, 2, 3, 4, 5 or 6. Within 6 steps a remainder comes up a second time, and from then on the same digits come round again. 1/7 uses all six remainders: 0.142857142857…
How do I turn a fraction into a percent?
Convert it to a decimal and multiply by 100: 3/8 = 0.375 = 37.5%. Or multiply the fraction by 100 directly: 1/3 × 100 = 33 1/3, so 1/3 = 33 1/3%.
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