Decimal to Fraction Calculator: Fast and Easy Conversions

Two Conversion Modes

This tool handles terminating decimals (like 0.625) and repeating decimals (like 0.1666...) with two different algorithms, selected by the "This is a repeating decimal" checkbox.

Worked Example: Terminating Decimal

Enter 0.625 with the checkbox unchecked. The decimal has 3 digits after the point, so the tool multiplies by 10 cubed: 0.625 x 1000 = 625, giving 625/1000. It then finds the greatest common divisor of 625 and 1000, which is 125, and divides both numbers by it: 625 / 125 = 5, 1000 / 125 = 8. Final answer: 5/8.

Worked Example: Repeating Decimal

Enter "0.1" in the decimal field, check the repeating box, and enter "6" as the repeating part (representing 0.1666...). The algebra behind this: let x = 0.1666..., then 10x = 1.666..., and 100x = 16.666.... Subtracting the first from the second isolates the repeating part: the tool computes numerator = 1 x (10 - 1) + 6 = 15 and denominator = 10 x (10 - 1) = 90, giving 15/90. Simplified by dividing both by their GCD of 15, that's 1/6 - which checks out, since 1 divided by 6 is 0.16666...

What "Non-Repeating Part" Means

For a decimal like 0.1666..., the "1" before the repeating "6" is the non-repeating part. Pure repeating decimals like 0.333... have no non-repeating part at all - you'd leave that field blank and just supply "3" as the repeating digits.

Sign Handling

Negative decimals are converted using their absolute value, and the minus sign is reattached to the final numerator - so -0.625 becomes -5/8, not 5/-8.