Convert a Decimal to a Fraction

Every decimal - and every decimal-like notation - hides an exact fraction. 0.75 is 3/4; 0.333... is exactly 1/3; 0.(142857) is exactly 1/7. Terminating decimals become fractions over powers of ten; repeating ones need a small algebraic trick. Either way the fraction is unique and the conversion is exact.

Convert a Decimal to a Fraction takes any decimal, including repeating forms, and returns the exact reduced fraction p/q with the working shown. Batch up to 1000 decimals per run, all exact, all reduced.

• Exact fractions: Every result reduced via the gcd.
• Repeating support: 0.(3), 0.1(6) and 0.333... all parsed.
• Steps shown: The method visible on every row.
• Any size: BigInt keeps huge decimals exact.
• Batch mode: Up to 1000 decimals per run.
• Copy or download: Export the fractions.

1. Enter a decimal - plain, with dots, or parenthesised repeat.
2. Optionally batch - one per line, up to 1000.
3. Generate - the exact reduced fraction appears.
4. Read the steps - how the fraction was built.
5. Copy or download - the results.

1. 0.75: 75/100 reduced to 3/4.

2. 0.333...: the repeating trick gives exactly 1/3.

3. 0.(142857): 142857/999999 reduces to exactly 1/7.

4. 2.5: 25/10 reduced to 5/2 - the mixed form preserved as an improper fraction.

5. 0.1(6): point-1 then forever-6 gives exactly 1/6.

• Always reduced: gcd at the core, lowest terms every time.
• Repeats included: The hard cases - 0.(142857) - convert exactly.
• Methods visible: Learn the algebra as you convert.
• Batch speed: Hundreds of decimals at once.
• Copy or download: Results export in one click.
• Private and free: All arithmetic stays in the browser; nothing is uploaded or logged.