Maths / Fractions
Decimal to Fraction Converter
Convert a decimal to a fraction in its simplest form and as a mixed number, including repeating decimals like 0.(3), with an optional limit on the denominator.
Decimal to Fraction Converter: A terminating decimal is the digits over a power of ten, reduced: 0.625 = 625/1000 = 5/8. A repeating decimal uses the standard algebra: for x = 0.1(6), 100x − 10x = 16.6… − 1.6… = 15, so x = 15/90 = 1/6. Digits are handled exactly, not as floating-point numbers. With a largest denominator, the nearest fraction is found from the number's continued fraction, the same method as Python's limit_denominator; ruler mode instead rounds to the nearest 1/2, 1/4, and so on up to 1/64. Runs 100% locally in your browser with zero server file uploads.
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For a repeating decimal, put the repeating digits in brackets: 0.(3) for 0.333…, 0.1(6) for 0.1666….
0.625 = 58
0.625 = 625 ÷ 1000, then divide both by their greatest common divisor.
Common conversions
0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.2 = 1/5, 0.125 = 1/8, 0.375 = 3/8, 0.(3) = 1/3, 0.(6) = 2/3, 0.1(6) = 1/6, 0.(142857) = 1/7. A fraction ends as a decimal only when its denominator, in lowest terms, has no prime factors other than 2 and 5.
For arithmetic with fractions, use the fraction calculator; to find common factors, prime factorisation.
Fractions for measuring
Imperial rulers mark sixteenths or thirty-seconds of an inch. Rounding to the nearest 1/16 turns a decimal measurement into the nearest mark: 0.4 in ≈ 3/8 in (6/16). A largest denominator of 16 gives a different answer, 2/5, because fifths are allowed too.
How to use it
- Type the decimal, such as 0.625; write repeating digits in brackets, such as 0.1(6).
- Read the fraction in its simplest form, and as a mixed number when it is above 1.
- For inches, round to the nearest 1/16; for a simpler fraction, set the largest denominator.
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Frequently asked questions
How do I convert 0.333… to a fraction?
Write it as 0.(3): it is exactly 1/3. Typing 0.333 gives 333/1000, which is close but not equal.
How do I get a fraction for a ruler or tape measure?
Choose Round to a ruler mark, nearest 1/16 (or 1/32, or 1/64): 0.3125 inches gives 5/16, and 0.4 inches rounds to 3/8, the nearest sixteenth mark.
Is π a fraction?
No: π is irrational, but 22/7 (denominator up to 10) and 355/113 (up to 1000) are close approximations.
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