Decimal to Fraction Converter

How the conversion actually works

This converter doesn't just read off decimal places and slap a power of 10 underneath — it runs a continued-fraction algorithm, which finds the smallest denominator that reproduces your decimal to within 1e-10. That matters because a naive "count the digits" approach on something like 0.142857142857 would produce an ugly fraction with a huge denominator, while the continued-fraction method correctly lands on 1/7.

Worked example

Enter 0.625:

• The algorithm expands 0.625 as a continued fraction and converges on numerator 5, denominator 8
• Result: 0.625 = 5/8
• Since 5 < 8, there's no whole-number part, so no mixed number is shown

For an improper case, entering 1.25 gives numerator 5, denominator 4 (5/4), and because 5 > 4 the tool also displays the mixed number 1 1/4.

Where approximation kicks in

If your input has more than 10 digits after the decimal point, the tool flags the result as an approximation rather than an exact match — this catches long repeating decimals like 0.3333333333333 that a computer can never represent exactly as a JavaScript floating-point number in the first place.