CALCULATOR
Decimal to Fraction
Convert a terminating or explicitly repeating decimal to a reduced exact fraction, a mixed-number view and verifiable conversion steps.
Exact fraction
Decimal approximation (not exact): 0.625
How this fraction is calculated
- Read the decimal
Treat 0.625 as a terminating decimal.
- Write a fraction
There are 3 decimal place(s), so use denominator 1000: 625/1000.
- Find the common factor
The greatest common divisor of 625 and 1000 is 125.
- Reduce the fraction
Divide 625 and 1000 by 125 to get 5/8.
How the calculation works
For a terminating decimal, use a power-of-ten denominator, then reduce by the greatest common divisor. For repeating notation, align and subtract matching repeating tails, then reduce.
Worked example
For “0.625” in terminating notation, the exact reduced fraction is 5/8.
Assumptions and limits
Use ordinary decimal text with a dot. Select repeating notation explicitly; the chosen number of final fractional digits repeats. Input is limited to 64 characters and 18 digits on each side of the decimal point, with absolute value at most 1000000000000.