🔁 Decimal ⇄ Fraction Converter
0.625 = 5/8, and 0.1666… = 1/6 exactly — this converter handles repeating decimals properly in both directions, showing the repetend in parentheses.
5/8
Exact fraction
62.5%
As a percent
Repeating decimals convert exactly: 0.1(6) means 0.1666… = 1/6, and 0.(3) = 1/3. Every fraction's decimal either terminates or repeats — this tool shows which, with the repetend in parentheses. Exact arithmetic, computed locally.
How the decimal ⇄ fraction converter works
Decimal to fraction: a terminating decimal like 0.625 becomes 625/1000 and reduces to 5/8; a repeating decimal written with parentheses — 0.1(6) for 0.1666… — is converted with the exact algebraic identity (multiply by powers of ten, subtract, solve), so 0.(142857) comes back as precisely 1/7. Fraction to decimal: long division runs with cycle detection on the remainders, so the tool doesn't just print digits — it identifies where the expansion starts repeating and writes the repetend in parentheses. Every fraction's decimal either terminates (when the reduced denominator has only factors 2 and 5) or repeats; this shows which, exactly.
The parenthesis notation is the key to exactness: 0.33 and 0.(3) are different numbers — 33/100 versus 1/3 — and a converter that ignores the difference quietly gives the wrong fraction. If you're converting a measured decimal (0.33 from a ruler), the terminating interpretation is what you want; if you're converting a mathematical one (0.333… from dividing by 3), write it as 0.(3).
Frequently asked questions
How do I enter a repeating decimal?
Put the repeating digits in parentheses: 0.(3) for 0.333…, 0.1(6) for 0.1666…, 1.2(45) for 1.2454545…. The conversion is then exact — 0.(3) gives 1/3, not 3333/10000.
How does decimal-to-fraction conversion work?
Terminating: put the digits over the matching power of ten and reduce (0.625 = 625/1000 = 5/8). Repeating: use the classic identity — for x = 0.(3), 10x − x = 3, so x = 3/9 = 1/3. The tool applies the general form of that algebra.
Which fractions give terminating decimals?
Exactly those whose reduced denominator contains no prime factors other than 2 and 5. 3/8 terminates (0.375); 1/6 cannot (0.1(6)) because of the factor 3.
How long can the repeating part be?
Up to one less than the denominator — 1/7 repeats every 6 digits, 1/97 every 96. The tool detects repetends up to 400 digits and says so if yours is longer.
Is anything uploaded?
No — conversion is exact integer arithmetic in your browser, offline-capable.
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