Decimal to Fraction Calculator
Convert any decimal to a simplified fraction and mixed number with step-by-step working, including repeating decimals like 0.333... and 0.1666...
About the Decimal to Fraction Calculator
This decimal to fraction calculator converts any decimal — 0.75, 2.375, even repeating decimals like 0.333... — into a fully simplified fraction and mixed number, and shows every step of the working, including the greatest common divisor (GCD) used to reduce the fraction.
For a terminating decimal, the method is to write the digits over a power of 10 and simplify: 0.625 = 625/1000, and since GCD(625, 1000) = 125, that reduces to 5/8. For repeating decimals, tick the repeating box and say how many trailing digits repeat: the calculator uses the standard nines method, so 0.333... becomes 3/9 = 1/3 and 0.1666... becomes (16 − 1)/90 = 15/90 = 1/6.
Students learning fractions, and anyone converting measurements (0.375 inches = 3/8), use this daily. Showing the GCD step makes it useful for checking homework, not just getting the answer.
How to Use the Decimal to Fraction Calculator
- 1Type the decimal, e.g. 0.625 or 2.4.
- 2If the last digits repeat forever (like 0.333...), tick the repeating box and enter how many digits repeat.
- 3Read the simplified fraction and mixed number.
- 4Follow the steps panel to see the power-of-10 setup and the GCD used to simplify.
Frequently Asked Questions
How do I convert 0.625 to a fraction?
Write it over a power of 10: 0.625 = 625/1000. The greatest common divisor of 625 and 1000 is 125, so divide both by 125 to get 5/8. The calculator shows exactly these steps for any terminating decimal.
How do I convert a repeating decimal like 0.333... to a fraction?
Each repeating digit contributes a 9 to the denominator. For 0.333... one digit repeats, so it equals 3/9, which simplifies to 1/3. For 0.121212... two digits repeat, giving 12/99 = 4/33. Tick the repeating checkbox and enter the number of repeating digits.
What about decimals where only some digits repeat, like 0.1666...?
Use one 9 per repeating digit and one 0 per non-repeating decimal digit. For 0.1666..., subtract the non-repeating part: (16 − 1) = 15 over 90, giving 15/90 = 1/6. Enter 0.1666 in the calculator, tick repeating, and set repeating digits to 1.
How do I convert a decimal bigger than 1, like 2.75?
The whole part stays: 2.75 = 275/100 = 11/4 as an improper fraction, or 2 3/4 as a mixed number. The calculator shows both forms so you can use whichever your homework or recipe needs.
Why does the calculator limit the number of digits?
It accepts up to 12 digits so every conversion stays exact. Beyond that, floating-point rounding could make the fraction slightly wrong. Twelve digits is more precision than almost any practical measurement or school problem requires.