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.
Worked through: 0.35 has two digits after the point, so the 35 becomes the numerator over a denominator of 100. The greatest common divisor of 35 and 100 is 5, and dividing both parts by 5 leaves 7/20. Nothing is rounded at any stage. The numerator and denominator that come back are whole numbers, so they can be used directly in fraction arithmetic.
The reverse operation is different in kind: it divides the numerator by the denominator, which is the step where an approximation appears. The Fraction to Decimal Calculator does that conversion, displaying up to 10 decimal places, so 1/3 reads as 0.3333333333.
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.
A decimal above one
1.25 has two decimal places, so it becomes 125/100, which simplifies to 5/4. The result is an improper fraction because the decimal was greater than one, and 5/4 is the same value as 1.25.
A decimal that reduces sharply
0.125 has three decimal places, so it becomes 125/1000. Dividing both parts by 125 gives 1/8, so a fraction with a single-digit numerator and denominator can stand for a decimal with several digits after the point.
Common uses
- Rewriting a decimal share of a quantity as a fraction of one, so the remaining working can be done exactly.
- Reducing a ratio written in decimals, such as 1.5:2.5, by converting each side first — the ratio calculator takes decimal sides and simplifies them in one step.
- Checking an answer that has to be given as a fraction in lowest terms, such as school or exam working.
- Converting a decimal saving or share into a fraction before entering it into a spreadsheet or formula that stores fractions.
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.
- Trailing zeros make no difference: 0.50 is the same number as 0.5, so both convert to 1/2.
- Very small decimals are handled by counting the digits written, so 0.0007 becomes 7/10000 rather than being rounded down to zero.