Fraction to Decimal Converter
Fraction or mixed number to decimal with the repeating block shown (1/7 = 0.(142857)), or a terminating, repeating or e-notation decimal to the exact fraction.
The exact decimal with its repeating block, a rounded value and the percentage; or the fraction in lowest terms and as a mixed number, plus the best simpler approximations under a denominator limit.
Example: 1/7 is 0.(142857), repeating every six digits; 0.375 is exactly 3/8; 2.1(6) is 13/6; 3.14159 with denominators up to 1 000 is best approximated by 355/113 (error 0.0000029).
Long division,
not floating point.
Why the decimal is exact, how the repeating block is found, and where the simpler fractions come from.
Fraction to decimal
The numerator is divided by the denominator digit by digit, as on paper, carrying the remainder. When a remainder repeats, the digits since its first appearance form the repeating block — 1/7 gives remainders 1, 3, 2, 6, 4, 5 and then 1 again, so the block is 142857. A denominator whose only prime factors are 2 and 5 terminates; any other never does. No floating-point number is involved, so 1/3 is 0.(3) rather than 0.333333333333333.
Decimal to fraction
A terminating decimal is its digits over a power of ten; a repeating block c of r digits after f fixed places adds c ÷ (10ᶠ·(10ʳ − 1)); e-notation and percent scale by powers of ten. The result is reduced by the greatest common divisor. Because the input is read as the text you typed, 0.1 is exactly 1/10 — the page never sees the binary value a calculator would store.
Simpler fractions
The continued-fraction convergents of the value are the best rational approximations with denominators up to your limit: 3.14159 gives 3, 22/7, 333/106, 355/113. The error column is exact. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Exact integer long division with remainder tracking for the repeating block; a decimal a.b(c) equals (a·10ᶠ + b)/10ᶠ + c/(10ᶠ·(10ʳ − 1)); approximations are continued-fraction convergents
Last reviewed 21 September 2026. How results are checked: How we verify.