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, 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.