Fractions are exact; decimals are easier to compare, type into a calculator or read off a ruler. This calculator converts any fraction or mixed number to a decimal. When the decimal repeats forever — like 1/3 — it shows the repeating digits in parentheses, gives a rounded value you can use, and simplifies the fraction too.
How to use the fraction to decimal calculator
- Enter the numerator (top number) and denominator (bottom number).
- For a mixed number such as 2 5/16, enter 2 as the whole number.
- Read the decimal, the rounded value, the percent and the simplified fraction.
Fraction to decimal formula
Mixed number: decimal = whole number + numerator ÷ denominator
The calculator uses long division and watches the remainders. When a remainder repeats, the digits from that point repeat forever, so it marks them as the repeating cycle.
Worked examples
- 3/8: 3 ÷ 8 = 0.375 (terminates)
- 2 5/16: 2 + 5 ÷ 16 = 2 + 0.3125 = 2.3125
- 5/6: 5 ÷ 6 = 0.8333… = 0.8(3) — only the 3 repeats
- 1/7: 0.(142857) — a six-digit repeating cycle
Common fractions as decimals
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/16 | 0.0625 |
| 1/3 | 0.333… | 3/16 | 0.1875 |
| 2/3 | 0.666… | 5/16 | 0.3125 |
| 1/4 | 0.25 | 7/16 | 0.4375 |
| 3/4 | 0.75 | 9/16 | 0.5625 |
| 1/5 | 0.2 | 11/16 | 0.6875 |
| 1/6 | 0.1666… | 13/16 | 0.8125 |
| 1/8 | 0.125 | 15/16 | 0.9375 |
| 3/8 | 0.375 | 1/32 | 0.03125 |
| 5/8 | 0.625 | 1/10 | 0.1 |
| 7/8 | 0.875 | 1/12 | 0.0833… |
Terminating or repeating?
Reduce the fraction to lowest terms and look at the denominator's prime factors. If they are only 2s and 5s — 2, 4, 5, 8, 10, 16, 20, 25, 32… — the decimal terminates. Any other prime factor (3, 7, 11…) makes it repeat. That's why sixteenths on a tape measure always convert cleanly, while thirds never do.
Where this comes up
- Measurements: converting fractional inches to decimal inches for a caliper or CNC machine.
- Recipes: turning ⅔ cup into 0.67 for a scale-up.
- Money and grades: 17/20 on a test is 0.85, or 85%.
Rounding a repeating decimal
Because a repeating decimal never ends, you must decide where to stop. The cleanest approach is to round at the precision your task needs: two decimal places for money (1/3 → 0.33), three or four for engineering. Remember that a rounded decimal is slightly off the true fraction, and the error can accumulate. Adding 0.33 three times gives 0.99, not 1, whereas 1/3 + 1/3 + 1/3 is exactly 1. When exactness matters in a chain of calculations, keep working with fractions and convert to a decimal only at the very end.
How the calculator finds the repeating part
It performs ordinary long division by hand, one digit at a time. After each step there is a remainder smaller than the denominator, so only a limited number of remainders are possible. As soon as a remainder shows up for the second time, the digits that follow must repeat the earlier sequence, which marks the start of the cycle. For a denominator d, the cycle can never be longer than d − 1 digits; 1/7 reaches that maximum with its six-digit cycle, 142857.
Going the other way? Use the Decimal to Fraction Calculator. Need a percentage? The Fraction to Percent Calculator does it in one step.
Frequently asked questions
How do I convert a fraction to a decimal?
Divide the numerator (top number) by the denominator (bottom number). 3/8 = 3 ÷ 8 = 0.375.
How do I convert a mixed number to a decimal?
Convert the fraction part and add the whole number. 2 5/16 = 2 + (5 ÷ 16) = 2 + 0.3125 = 2.3125.
What is a repeating decimal?
A decimal whose digits repeat forever, such as 1/3 = 0.333… or 1/7 = 0.142857142857… This calculator shows the repeating part in parentheses: 0.(3) and 0.(142857). Some textbooks write it with a bar over the repeating digits instead.
Which fractions give terminating decimals?
A fraction in lowest terms ends (terminates) only if its denominator has no prime factors other than 2 and 5. So 3/8, 7/20 and 9/25 terminate, while 1/3, 5/6 and 2/7 repeat.
What is 5/8 as a decimal?
0.625. Common eighths: 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.