Convert a fraction to a decimal and a percentage, with long division.
Type a fraction into the fraction to decimal calculator and you get the exact decimal, with any repeating digits marked, plus the same value as a percentage. The long division is shown step by step, so you can see where each digit comes from and why some decimals stop while others repeat forever.
Quick answer: to convert a fraction to a decimal, divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. If the division never ends, the digits repeat: 1/3 = 0.333…
How to Use the Fraction to Decimal Calculator
- Enter the numerator, the top number.
- Enter the denominator, the bottom number.
- Read the results:
- Decimal: the exact value. A line over digits means they repeat.
- Rounded: the value to 6 decimal places.
- Percentage: the decimal × 100.
- Type: terminating or repeating.
Both numbers must be whole numbers. For a mixed number such as 2 3/8, convert it to an improper fraction first with the mixed number calculator, or work out 3/8 and add 2.
How to Convert a Fraction to a Decimal
Divide the numerator by the denominator.
Decimal = Numerator ÷ Denominator
When the division does not come out evenly, use long division. Add a zero to the remainder, divide again, and repeat. If a remainder comes up that you have already seen, the digits from that point repeat forever.
Fraction to Decimal Examples
3/8. 3 ÷ 8 = 0.375, a terminating decimal. As a percentage, 37.5%.
5/12. 5 ÷ 12 = 0.41666…, with the 6 repeating forever. As a percentage, 41.6667%.
2/7. 2 ÷ 7 = 0.285714285714…, so the block 285714 repeats.
7/16. 7 ÷ 16 = 0.4375.
Inch Fractions to Decimals
Tape measures, drill bits and wrenches use sixteenths of an inch, while plans and digital tools use decimals.
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/16 | 0.0625 | 9/16 | 0.5625 |
| 1/8 | 0.125 | 5/8 | 0.625 |
| 3/16 | 0.1875 | 11/16 | 0.6875 |
| 1/4 | 0.25 | 3/4 | 0.75 |
| 5/16 | 0.3125 | 13/16 | 0.8125 |
| 3/8 | 0.375 | 7/8 | 0.875 |
| 7/16 | 0.4375 | 15/16 | 0.9375 |
| 1/2 | 0.5 | 1 | 1.0 |
Which Fractions Give a Repeating Decimal?
Simplify the fraction, then look at the prime factors of the denominator.
- Only 2s and 5s (such as 2, 4, 5, 8, 10, 16, 20, 25): the decimal terminates.
- Any other prime factor (such as 3, 6, 7, 9, 11, 12): the decimal repeats.
That is why 3/8 ends after three digits, but 1/3 never ends. The prime factorization calculator shows the factors of any denominator.
Common Fractions as Decimals
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666… | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 1/16 | 0.0625 | 6.25% |
Converting the Other Way
To turn a decimal back into a fraction, including repeating decimals, use the decimal to fraction calculator. To add or multiply fractions before converting, use the fraction calculator.
Fraction to Decimal FAQs
How do you convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. 3/8 = 0.375, which is 37.5%.
How do you write a repeating decimal?
Put a bar over the digits that repeat. 5/12 is written 0.416 with a bar over the 6. You can also write 0.41666… with dots.
Why does my calculator show 0.6666667 for 2/3?
Most calculators run out of digits and round the last one. The true value is 0.666… with the 6 repeating forever.
Can I enter a negative fraction?
Yes. Enter a minus sign on the numerator or the denominator, and the decimal will be negative.
How we checked this page: every conversion was checked by long division and matches the calculator, including the repeating decimals.