Decimal to Fraction Calculator
Type any terminating decimal — 0.375, 2.5, −0.08 — and get the fraction in lowest terms, with the place-value steps and the mixed-number form when there's a whole part.
How a decimal becomes a fraction
A decimal is already a fraction in disguise: the digits after the point are counted in tenths, hundredths, thousandths… So write them over the matching power of ten, then reduce by the greatest common factor:
This works for terminating decimals. Repeating decimals (0.333…) need a different trick — multiplying by a power of 10 and subtracting — and some, like 0.333… = 1/3, can't be written over a power of ten at all. Support for repeating decimals is planned.
Worked examples
Example 1: 0.375 to a fraction
Convert 0.375.
- Three decimal digits → write over 1,000.0.375 = 375/1000
- Reduce by the GCF of 375 and 1000, which is 125.375/1000 = 3/8
0.375 = 3/8.
Example 2: a decimal over 1 — mixed number
Convert 2.6.
- The decimal part: one digit → tenths.0.6 = 6/10 = 3/5
- Attach the whole part.2 3/5 = 13/5
2.6 = 2 3/5 (or 13/5 as an improper fraction).
Example 3: drill bits — 0.3125 inch
A 0.3125-inch drill bit — which fractional size is it?
- Four digits → ten-thousandths.0.3125 = 3125/10000
- Reduce by 625.3125/10000 = 5/16
5/16 inch — a standard imperial bit size.
FAQ
How do I convert a repeating decimal like 0.666…?+
Set x = 0.666…, then 10x = 6.666…; subtracting gives 9x = 6, so x = 2/3. The over-a-power-of-ten method only works for decimals that end; this calculator currently handles terminating decimals.
Why does 0.50 show as 50/100 before reducing?+
The calculator respects the digits you typed: two decimal places means hundredths. After reducing by the GCF (50), the answer is the same 1/2 — the steps just start from your exact input.
What denominator will my decimal have?+
Always a divisor of a power of ten, i.e. built only from 2s and 5s: halves, quarters, fifths, eighths, tenths, sixteenths… A decimal can never reduce to thirds or sevenths — those repeat.
How do I go the other way, fraction to decimal?+
Divide the numerator by the denominator: 3/8 = 0.375. Our fraction calculator shows every result in decimal form alongside the fraction.
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