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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.

Calculate

Use a finite decimal or scientific notation (e.g. 1.5, 0.33333333333333, 1e-2).
When checked, the result is reduced using math.format on the fraction object.

Result

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.

Disclaimer. RapidRatio is informational only. It is not financial, tax, business, or professional advice. Verify results and assumptions with qualified professionals before making decisions.