Fraction Calculator — Fraction to Decimal Converter
The conversion view: enter any fraction and get its decimal value to six places, plus the answer a rounded decimal hides — whether the expansion terminates (5/8 = 0.625, exactly) or repeats forever (2/3 = 0.666…, displayed as ≈0.666667). The converter reduces the fraction first and reads the terminating test off the reduced denominator, so equivalent fractions like 9/12 and 3/4 always agree.
Fractions
Decimal
0.375
3/8 reduces to 3/8 · terminating decimal — this value is exact
Exact integer arithmetic — every result is reduced with the greatest common divisor, never a floating-point approximation. The decimal line is a 6-place display value; repeating decimals are marked with ≈. Everything calculates in your browser.
A fraction is a long-division problem
The decimal form of a fraction is just its numerator long-divided by its denominator. For 5/8, dividing 5.000 by 8 gives 0.625 and the remainder hits zero — the decimal terminates. For 2/3 the remainder never clears: every step leaves remainder 2 again, so the digit 6 repeats forever and no finite decimal is exact.
That is why the converter labels each result. A terminating answer like 0.375 for 3/8 is the exact value; a repeating answer like ≈0.333333 for 1/3 is a six-place display of a number whose true expansion never ends.
The terminating test
Reduce the fraction, then factor the denominator. If only 2s and 5s appear, the decimal terminates; any other prime makes it repeat. 7/16 has denominator 2⁴, so it terminates at 0.4375. 5/12 carries a factor of 3, so it repeats: ≈0.416667.
Always reduce first — the test reads the reduced denominator. 9/12 looks doomed because 12 contains a 3, but it reduces to 3/4, whose denominator is 2², so it terminates cleanly at 0.75.
Equivalents worth knowing by heart
The everyday fractions convert as follows: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875, and 1/16 = 0.0625. The thirds are the famous repeaters — 1/3 ≈ 0.333333 and 2/3 ≈ 0.666667 — which is why recipes and measurements built on thirds never round perfectly.
Questions
- Is 1/3 as a decimal just 0.33?
- No — 1/3 is 0.333… repeating forever. The converter shows it rounded to six places (0.333333) and labels it repeating so the rounding is explicit.
- How can I tell whether a fraction terminates without converting it?
- Reduce it, then factor the denominator: only 2s and 5s means it terminates. 7/16 (denominator 2⁴) terminates at 0.4375; 5/12 repeats because of its factor of 3.
- What is 7/8 as a decimal?
- 0.875, exactly — 8 is 2³, so the decimal terminates.