Decimal to Fraction Calculator
Type a decimal such as 0.375, or a repeating one such as 0.(3) or 0.1666…, to get the exact fraction with the working.
For a repeating decimal, put the repeating part in brackets, 0.1(6), or end it with …, as in 0.333…
0.375 as a fraction
3/8
0.375 = 3/8 in lowest terms.
- As a percentage
- 37.5%
How to convert a decimal to a fraction
For a decimal that ends, write the digits after the point over a power of ten: one decimal place over 10, two over 100, three over 1,000. Then simplify. 0.375 has three places, so it is 375/1000, and dividing both by their GCF of 125 gives 3/8.
A repeating decimal needs a little algebra. Call it x. For 0.1666…, 10x = 1.666… and 100x = 16.666…; the two share the same endless tail, so subtracting cancels it: 100x − 10x = 90x = 15, and x = 15/90 = 1/6. The rule of thumb: a block of n repeating digits ends up over n nines (0.(27) = 27/99 = 3/11).
If you type 0.3333 the calculator treats it as exactly 3,333/10,000, because that is what the digits say, and offers the repeating reading 0.(3) = 1/3 if you meant a third. Typing 0.333… with dots reads the last digit as repeating.
0.d₁d₂…dₖ = d₁d₂…dₖ / 10ᵏ · 0.(r₁…rₙ) = r₁…rₙ / (10ⁿ − 1)
- Every repeating decimal is a rational number (a fraction of whole numbers), and every fraction’s decimal either terminates or repeats. Source: Wikipedia, Repeating decimal.
Decimals as fractions
Terminating and repeating decimals (repeating blocks in brackets) in lowest terms.
| Decimal | Fraction | Percent |
|---|---|---|
| 0.1 | 1/10 | 10% |
| 0.125 | 1/8 | 12.5% |
| 0.2 | 1/5 | 20% |
| 0.25 | 1/4 | 25% |
| 0.3 | 3/10 | 30% |
| 0.375 | 3/8 | 37.5% |
| 0.4 | 2/5 | 40% |
| 0.5 | 1/2 | 50% |
| 0.6 | 3/5 | 60% |
| 0.625 | 5/8 | 62.5% |
Show all 24 rowsShow fewer
| 0.7 | 7/10 | 70% |
| 0.75 | 3/4 | 75% |
| 0.8 | 4/5 | 80% |
| 0.875 | 7/8 | 87.5% |
| 0.9 | 9/10 | 90% |
| 0.(3) | 1/3 | 33.33% |
| 0.(6) | 2/3 | 66.67% |
| 0.1(6) | 1/6 | 16.67% |
| 0.8(3) | 5/6 | 83.33% |
| 0.(09) | 1/11 | 9.09% |
| 0.(142857) | 1/7 | 14.29% |
| 1.5 | 1 1/2 | 150% |
| 2.25 | 2 1/4 | 225% |
| 3.(3) | 3 1/3 | 333.33% |
Frequently Asked Questions
What is 0.6 as a fraction?
0.6 = 6/10, which simplifies to 3/5. But 0.666… (repeating) is 2/3, a different number.
Is 0.999… really equal to 1?
Yes. With x = 0.999…, 10x = 9.999…, so 9x = 9 and x = 1. Two decimals that agree forever with no gap between them are the same number.
How do I convert a decimal bigger than 1?
The same way; the whole part comes along. 2.25 = 225/100 = 9/4, which is 2 1/4 as a mixed number.