Fraction to Decimal Calculator
Type a fraction or mixed number to get the exact decimal, whether it repeats, the percent and a rounded value, with the long-division reasoning.
Free, no sign-upRuns in your browserHow we calculate
Leave empty for a plain fraction; use it for 2 3/4.
- Rounded to 4 places
- 0.3750
- As a percent
- 37.5%
- Lowest terms
- 3/8
- Type
- Terminating
How this was calculated
- Divide the numerator by the denominator: 3 ÷ 8 = 0.375.
- The denominator 8 = 2³ has no prime factor besides 2 and 5, so the decimal terminates after 3 digits.
Common fractions as decimals
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) | 33.3333% |
| 2/3 | 0.(6) | 66.6667% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1(6) | 16.6667% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/16 | 0.0625 | 6.25% |
How to convert a fraction to a decimal
A fraction is a division in disguise: the bar means "divided by". To convert a fraction to a decimal, divide the numerator by the denominator. 3/8 is 3 ÷ 8 = 0.375, and 7/4 is 7 ÷ 4 = 1.75. For a mixed number such as 2 3/4, convert only the fraction part and add the whole number: 2 + 0.75 = 2.75. This fraction to decimal calculator does the long division with exact whole-number arithmetic, so it also tells you when the digits never stop.
Worked example: 5/12
Divide 5 by 12. 12 does not go into 5, so write 0 and bring down a zero: 50 ÷ 12 = 4 remainder 2. Bring down another zero: 20 ÷ 12 = 1 remainder 8. Then 80 ÷ 12 = 6 remainder 8. The remainder 8 has appeared before, so the 6 repeats forever: 5/12 = 0.41666…, written 0.41(6). To get a percent, multiply by 100: 41.67% (rounded). The steps under the result show the same reasoning for any fraction you enter.
Terminating or repeating?
Reduce the fraction to lowest terms and look at the denominator. If its only prime factors are 2 and 5, the decimal ends: 1/8 (2 × 2 × 2) is 0.125 and 3/20 (2 × 2 × 5) is 0.15. Any other prime factor, such as the 3 in 1/6 or the 7 in 1/7, makes the decimal repeat. The block can be long: 1/7 repeats the six digits 142857, and 1/17 repeats sixteen. The calculator reduces first, so 6/8 is correctly treated as 3/4 = 0.75.
Common mistakes
- Dividing the wrong way round. It is top ÷ bottom: 1/4 is 1 ÷ 4 = 0.25, not 4 ÷ 1.
- Calling 0.33 "one third". 1/3 is 0.333… without end; 0.33 is only an approximation and 0.33 = 33/100.
- Dropping the whole number. 1 1/2 is 1.5, not 0.5.
When the rounded result misleads
Rounding a repeating decimal and converting it back rarely returns the original fraction: 0.667 is 667/1000, not 2/3. Keep the fraction while you calculate and round only at the end. To go the other way, use the decimal to fraction calculator; for a percent of a number, the percentage calculator.
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the numerator (top) by the denominator (bottom). 3/8 = 3 ÷ 8 = 0.375, and 5/4 = 1.25.
How do you convert a mixed number to a decimal?
Convert the fraction part and add the whole number. 2 3/4 = 2 + 3 ÷ 4 = 2 + 0.75 = 2.75.
Which fractions give repeating decimals?
A fraction in lowest terms repeats whenever its denominator has a prime factor other than 2 or 5. 1/3 = 0.333…, 1/6 = 0.1666… and 1/7 = 0.142857142857…, while 1/8 and 3/20 terminate.
How do you turn a fraction into a percent?
Convert it to a decimal and multiply by 100. 3/8 = 0.375 = 37.5%.
What is 1/3 as a decimal?
0.333…, written 0.(3) with the 3 repeating forever. Rounded, it is 0.33 or 0.3333; it never equals exactly 0.33.
What is 5/8 as a decimal?
0.625. Eighths are 0.125, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.875.