How to convert a decimal to a fraction
- Type the decimal in Decimal number. The page opens with 0.75.
- If some digits repeat forever, put the repeating digits in Repeating digits (optional). For 0.1666... type 0.1 in the first box and 6 in the second.
- Read the Fraction in simplest form and the Mixed number. The Steps list shows the working.
- Check the tape-measure table for the nearest 1/8, 1/16, 1/32 and 1/64.
- To go the other way, use Fraction to decimal.
How the conversion works
A terminating decimal is the digits written over a power of ten, then reduced by the greatest common divisor (GCD). For 2.375, the digits 2375 go over 1000, the GCD is 125, and the result is 19/8, or 2 3/8 as a mixed number. For a repeating decimal, multiply by the powers of ten that line up the repeating block, subtract, and solve. With A the digits before the repeat, AB those digits plus one repeat, n the count of non-repeating places and k the repeat length, the value is (AB - A) / (10^n Ć (10^k - 1)). The arithmetic is exact, with no floating-point rounding.
Worked example: 0.75
With the default input the tool counts 2 decimal places and writes 75/100. The GCD of 75 and 100 is 25, so it shows 3/4 as both the fraction and the mixed number. The tape-measure table reads exact for every size, and the Fraction to decimal box shows 3/4 = 0.75 = 75%.
Decimal to fraction chart
| Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|
| 0.0625 | 1/16 | 0.4375 | 7/16 |
| 0.125 | 1/8 | 0.5 | 1/2 |
| 0.1875 | 3/16 | 0.5625 | 9/16 |
| 0.25 | 1/4 | 0.625 | 5/8 |
| 0.3125 | 5/16 | 0.75 | 3/4 |
| 0.375 | 3/8 | 0.875 | 7/8 |
Decimal inches on a tape measure
A tape measure marks inches down to sixty-fourths, so a decimal inch usually needs rounding. The tape-measure table rounds to the nearest 1/8, 1/16, 1/32 and 1/64 (ties round up) and says how far off each is. For 0.3 inch the nearest 1/16 is 5/16, rounded up by 0.0125, and the nearest 1/64 is 19/64. A value like 0.4375 is exactly 7/16.
Limits and edge cases
The tool converts exactly what you type, so 0.333 becomes 333/1000, not 1/3. When the exact fraction has a denominator above 100, a "Closest simple fraction" line suggests the nearest fraction with a smaller denominator. A minus sign carries through, and a comma works as a decimal comma (0,5) or a thousands separator (1,000). Numbers are limited to 25 digits before the point and 30 after, and scientific notation is not accepted. For arithmetic on fractions use the fraction calculator, for percentages the percentage calculator, and for inches and millimeters the length converter.
Frequently asked questions
How do you convert a decimal to a fraction?
Write the digits after the decimal point over 1 followed by that many zeros, then divide the top and bottom by their greatest common divisor. For 0.625, 625/1000 reduces to 5/8.
How do I turn 0.333... into 1/3?
Type 0 in the decimal box and 3 in Repeating digits. The tool treats the 3 as repeating forever and shows 1/3. Typing 0.333 with no repeating digits gives 333/1000, which is exactly what you typed.
How do I convert a decimal to a fraction in inches?
Use the tape-measure table. It rounds your decimal to the nearest 1/8, 1/16, 1/32 and 1/64 and shows how far off each one is. For example, 0.4375 is exactly 7/16.
How do I turn a fraction into a decimal?
Divide the numerator by the denominator. The Fraction to decimal box does this exactly and shows repeating decimals, so 1/3 reads 0.3333333333 (rounded) with the repeating form 0.(3).
What is the difference between a mixed number and an improper fraction?
An improper fraction has a numerator larger than its denominator, such as 19/8. A mixed number splits out the whole part, so 19/8 is 2 3/8. The tool shows both for any decimal above 1.
Sources: Wolfram MathWorld: Repeating Decimal for the repeating-decimal formula.