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Decimal to Fraction Calculator

Turn a decimal such as 0.375 into a simplified fraction, write repeating decimals like 0.1(6) exactly, or find the closest simple fraction to a long decimal such as 3.14159.

By Adzita Editorial Team · Updated 2026-11-03 · How we build and check our tools

Terminating decimals

A decimal that ends is already a fraction with a power of ten underneath. Count the digits after the point, put the digits over 1 followed by that many zeros, then simplify. For 0.375 there are three decimal places, so it equals 375/1000. The greatest common factor of 375 and 1000 is 125, which leaves 3/8.

Simplifying divides the top and bottom by their greatest common factor, found with the Euclidean algorithm. The tool shows the factor it removed, so you can verify the step by hand. A decimal with a whole-number part, such as 2.75, becomes the improper fraction 11/4 or the mixed number 2 3/4.

Repeating decimals written in brackets

A repeating decimal is also exactly rational. Suppose a decimal has k digits that do not repeat and a block of m digits that does. The value equals (whole digits through the first block − whole digits before the block) ÷ (10k × (10m − 1)). For 0.1(6) the non-repeating part is 1, the full string is 16, so the numerator is 16 − 1 = 15 and the denominator is 10 × 9 = 90. Simplifying 15/90 gives 1/6.

The special case 0.(9) yields 9/9, which is exactly 1. That surprising equality is true, not a rounding trick: both are the same real number.

Approximating long decimals

A value like 3.14159 is a rounded measurement, not an exact decimal that came from a simple fraction. Converted exactly it becomes 314159/100000, which is correct but not useful. In approximate mode the tool tests every denominator up to your limit, rounds the numerator for each, and keeps the fraction with the smallest error. With a limit of 100, 3.14159 gives 311/99; with a limit of 10 it gives 22/7.

Raise the limit for more accuracy. The error line reports how far the fraction is from your decimal. Small denominators are handy for woodworking tape measures (limit 16 or 64) or recipe quantities (limit 8).

Common mistakes and how to avoid them

• Typing a rounded repeat. 0.333 is exactly 333/1000, not 1/3. Use 0.(3) for the true repeating value.
• Forgetting to simplify. 50/100 and 1/2 are equal, but most answers should be in lowest terms.
• Sign confusion. A negative decimal gives a negative fraction, with the minus sign on the whole mixed number.
• Percent inputs. To convert 12.5%, divide by 100 first and enter 0.125.

To check any answer, divide the numerator by the denominator on a calculator and compare with your original decimal. For repeating input the check value will show twelve significant figures, so a repeat such as 0.1(6) appears as 0.166666666667.

Worked example

The decimal 0.1666... repeats the digit 6 forever. Written as 0.1(6), it converts to an exact fraction of one sixth.

Inputs

Result

Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.

Frequently asked questions

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