How the conversion works

Every terminating decimal is a fraction whose denominator is a power of 10. The number of digits after the decimal point tells you which power to use.

For example, 0.750.75 becomes rac{75}{100} because there are two decimal places. After that, divide the numerator and denominator by their greatest common divisor to simplify.

The place-value rail on this page shows why extra decimal digits create larger base denominators before the simplification step reduces them.

When this is useful

  • Checking homework steps when a decimal answer must be reported as a fraction.
  • Converting measurements like 1.251.25 into more exact fractional forms.
  • Seeing whether a decimal simplifies cleanly or already sits in lowest terms.