How it works
The decimal is scaled up to a whole number using however many digits follow the decimal point, placed over the matching power of 10, then reduced by the greatest common divisor — so the conversion is exact, not an approximation.
Formula: A decimal with n digits after the point becomes (that whole number) / 10ⁿ, then simplified.
Examples
A common decimal
0.75 has two decimal places, so it becomes 75/100, which simplifies to 3/4.
A tenths decimal
0.6 becomes 6/10, which simplifies to 3/5.
Things to keep in mind
- A whole number, such as 2, converts to a whole-number fraction, 2/1.
- A negative decimal converts to a fraction with a negative numerator, such as −0.75 to −3/4.
- An extremely precise decimal (many digits after the point) may be too precise to convert exactly and is rejected rather than rounded silently.