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Decimal To Fraction Converter
Enter a decimal number (for example 0.125). Inputs are parsed with RapidRatio’s BigNumber pipeline; the fraction itself comes from math.fraction and, when simplification is on, math.format of that fraction. Long tails like 0.33333333333333 are mapped to simple rationals such as 1 / 3 when a plain floating value represents them. When |x| > 1 and there is a fractional part, a second line shows the equivalent mixed number.
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How to Convert a Decimal to a Fraction
On paper you can turn a terminating decimal into a fraction in three steps—this mirrors what many teachers show in middle school before you reduce.
- Write the decimal over 1—for example, 0.125 becomes 0.125 / 1.
- Multiply top and bottom by a power of 10—use one factor of 10 for every digit after the decimal point. Here there are three digits, so multiply by 1000: 125 / 1000.
- Simplify the fraction—divide numerator and denominator by their greatest common divisor until no common factor remains (for 125 / 1000, the GCD is 125, giving 1 / 8). In this tool, leave Simplify fraction checked to see the same fully reduced form via math.format.
Repeating decimals and “almost repeating” digits
A true repeating decimal needs infinitely many digits; calculators and homework answers often show a long but finite run instead (like many threes after the decimal point). After your value is validated as a BigNumber, we pass a floating value into math.fraction so close rational approximations such as 0.33333333333333 can resolve to a simple fraction like 1 / 3. If you uncheck Simplify, you get the unreduced “multiply by 10ⁿ” form from the displayed decimal digits instead.
Mixed numbers
When the absolute value of your decimal is greater than 1 and the improper fraction is not a whole number, a second line shows a mixed number (for example 1.5 as 1 1 / 2 while the main line stays 3 / 2). Integers such as 2 only appear as a single fraction line.
FAQ
What is 0.625 as a fraction?
0.625 equals 5/8. Write it as 625/1000 (three decimal places), then divide numerator and denominator by their greatest common divisor, 125, to obtain 5/8.
How do you simplify a fraction?
Factor the numerator and denominator, then cancel common factors—or divide both by their greatest common divisor (GCD) until no common factor except 1 remains. With this tool, checking Simplify uses math.format on the fraction object so the result is shown in lowest terms.