Converting a fraction to a decimal means doing the division that the fraction bar stands for. Some fractions, such as 3/8, divide out to a decimal that ends. Others, such as 5/6, produce a digit or a block of digits that repeats forever. This calculator divides exactly, shows each remainder so you can see where the repetition begins, marks the repeating block, and also gives a rounded value.
How to use the converter
- Enter the fraction. Use the left box for the whole part of a mixed number.
- Choose how many decimal places to round to.
- The tape shows the exact decimal with any repeating digits under a bar, the rounded value, the percent and the fraction in lowest terms. The note explains why the decimal terminates or repeats.
- Under the steps, the long-division layout shows the division carried out one digit at a time.
The method
- Divide the numerator by the denominator. The quotient is the whole-number part.
- Multiply the remainder by 10 (bring down a 0) and divide again; that quotient is the next decimal digit.
- Repeat. If the remainder becomes 0, the decimal terminates. If a remainder appears a second time, the digits from that point repeat.
Worked example: 5/6
- 5 ÷ 6 = 0, remainder 5. The decimal starts 0.
- 50 ÷ 6 = 8, remainder 2 → 0.8
- 20 ÷ 6 = 3, remainder 2 → 0.83
- The remainder 2 has appeared before, so the 3 repeats forever: 5/6 = 0.8333… = 0.83̅.
Rounded to four decimal places, 5/6 ≈ 0.8333; as a percent it is 83.3̅%.
Why only 2s and 5s terminate
A terminating decimal is a fraction with a power of 10 as its denominator, like 375/1000. Since 10 = 2 × 5, a fraction can be rewritten over a power of 10 only if its own denominator, in lowest terms, is built from 2s and 5s. For 3/8, 8 = 2³, so 3/8 = 375/1000 = 0.375. For 5/6, the factor 3 in 6 = 2 × 3 can never be cleared, so the decimal repeats.
Common fractions
| Fraction | Decimal | Type |
|---|---|---|
| 1/4 | 0.25 | terminates |
| 3/8 | 0.375 | terminates |
| 1/3 | 0.3̅ | repeats (1 digit) |
| 5/6 | 0.83̅ | repeats after 1 digit |
| 1/7 | 0.142857 repeating | repeats (6 digits) |
| 1/11 | 0.09 repeating | repeats (2 digits) |
| 1/12 | 0.083̅ | repeats after 2 digits |
Rounding a repeating decimal
To round, look at the digit after the last place you keep: 5 or more rounds up. 2/3 = 0.6666… rounds to 0.67 at two places and 0.6667 at four. Keep the exact fraction for further calculations if you can, and round only the final answer. For a full chart of fractions up to 64ths, see the fraction to decimal chart; to reverse the process, including repeating decimals, use the decimal to fraction calculator. Dividing decimals by decimals works the same way in the long division with decimals calculator.
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For 3/8, divide 3 by 8: 3.000 ÷ 8 = 0.375. Long division works for any fraction; add zeros after the decimal point until the remainder is 0 or starts repeating.
How can I tell if a fraction will give a repeating decimal?
Reduce the fraction to lowest terms and look at the denominator. If its only prime factors are 2 and 5, the decimal terminates. Any other prime factor, such as 3, 7 or 11, makes it repeat.
What does the bar over a digit mean?
It marks the digits that repeat forever. 0.83̅ means 0.8333…, where only the 3 repeats. The same number can be written 0.8(3) in parenthesis notation.
How long can the repeating part be?
For a fraction in lowest terms with denominator d, the repeating block has at most d − 1 digits. 1/7 repeats every 6 digits and 1/97 repeats every 96 digits.