Decimal to Fraction Calculator
Convert terminating and repeating decimals to exact, fully reduced fractions.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this decimal to fraction calculator
- Type any decimal number into the input field — for example, 0.75, -1.5, or 3.14.
- For a repeating decimal, wrap the repeating block in parentheses directly after the decimal point: type 0.(3) for 0.333..., or 0.1(6) for 0.1666..., or 1.(09) for 1.090909...
- Press "Convert to Fraction" (or hit Enter) to see the exact simplified fraction, the mixed-number form when the value is greater than one, and a label confirming whether the decimal terminates or repeats.
- Check the decimal confirmation row to verify the fraction matches the number you entered.
- Use "Copy result" to send the fraction to your clipboard, or "Reset" to clear the field and start a fresh conversion.
About this decimal to fraction calculator
Every decimal can be expressed as an exact fraction. The method depends on whether the decimal terminates or repeats.
Terminating decimals — those with a finite number of digits after the decimal point — convert by writing the digits over the appropriate power of ten and then reducing. For example, 0.75 has two decimal places, so it becomes 75/100. Dividing both parts by their greatest common divisor (25) gives 3/4. In general, a decimal with k digits after the point equals its digit string over 10^k, simplified.
Repeating decimals use the parenthesis (repetend) notation to mark the block that cycles forever. The conversion formula is: let p be the count of non-repeating digits after the decimal and q be the length of the repeating block. The fraction equals (concat of non-repeating and repeating digits minus non-repeating digits alone) over (10^q - 1) times 10^p, plus the integer part over the same denominator, all simplified. For 0.(3), p = 0 and q = 1, giving (3 - 0) / (9 x 1) = 3/9 = 1/3. For 0.1(6), p = 1 and q = 1, giving (16 - 1) / (9 x 10) = 15/90 = 1/6.
After conversion the tool always reduces the fraction to lowest terms using the Euclidean GCD algorithm, so the result is always in its simplest form.
FAQ
- How do you convert a decimal to a fraction?
- Write the decimal digits over a power of ten matching the number of decimal places, then simplify by dividing numerator and denominator by their greatest common divisor. For instance, 0.6 = 6/10 = 3/5. For repeating decimals a slightly different algebraic formula is used — see the explanation above.
- How do I enter a repeating decimal?
- Place the repeating block inside parentheses immediately after the decimal point. Type 0.(3) for 0.333..., 0.1(6) for 0.1666..., 1.(09) for 1.090909..., and 0.(142857) for 0.142857142857... The tool reads the parentheses as the repetend and applies the exact algebraic formula.
- What fraction is 0.333... (written as 0.(3))?
- It is exactly 1/3. Using the repetend formula with p = 0 non-repeating digits and q = 1 repeating digit: (3 - 0) / (10^1 - 1) = 3/9, which simplifies to 1/3.
- Does the calculator reduce the fraction to lowest terms automatically?
- Yes. Every result is simplified using the Euclidean GCD algorithm, so the numerator and denominator share no common factor greater than one. You will never see an answer like 6/8 — it will always appear as 3/4.
- Can it convert decimals greater than 1 to a mixed number?
- Yes. When the resulting fraction is improper (numerator larger than denominator), the tool also shows the equivalent mixed number — a whole-number part alongside a proper fraction. For example, 1.625 converts to the improper fraction 13/8 and to the mixed number 1 5/8.
- Is the calculator free and private?
- Yes, it is completely free with no registration required. All calculations run locally in your browser; no numbers you enter are sent to any server.