Decimal to fraction converter

What inputs are accepted and how repeating decimals are written

Finite decimals such as 0.75, 2.5, and -0.125, as well as whole numbers such as 7, are converted with exact place-value arithmetic: seventy-five hundredths becomes seventy-five over one hundred and then reduces by the greatest common divisor to three over four. For repeating decimals, use the unambiguous parentheses notation taught in many textbooks: write 0.(3) for zero point three repeating, 0.1(6) for zero point one six repeating, or 1.(3) when the integer part is non-zero. You may also write a clear ellipsis form such as 0.333... when the repeating run is obvious; the engine detects a trailing single digit repeated at least three times or a multi-digit period that appears at least twice at the end of the fractional part. Send the required field value as a JSON number or, preferably, a numeric string so the digits you type are the digits that are converted. Aliases n, number, decimal, and input are accepted for the same field so forms and SDK snippets stay readable. Non-numeric text, empty strings, and incomplete fragments fail with invalid_input and are not charged. Digit length is capped for Worker isolate safety while still covering every classroom example and most engineering magnitudes you would type by hand. Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.

Reading numerator, denominator, fraction string, and method labels

The simplified flag is always true because reduction runs on every path; sign is -1, 0, or 1 so UIs can style negatives without reparsing the fraction string. A decimal field reconstructs a short preview of the reduced rational, using parentheses when long division finds a cycle, which is handy for confirming that 1/6 appears as 0.1(6). Use numerator and denominator when grading software must check each part; use fraction when a report needs a single token; use method when logs should record which algorithm path produced the answer. On success the response echoes the value you sent, a signed integer numerator, a positive integer denominator already reduced to lowest terms, and a fraction string such as 3/4 or -7/2 for quick display. When the input used parentheses or a detected ellipsis period, is_repeating is true and method is repeating_parentheses or repeating_ellipsis; finite digit strings use exact_decimal; bare JSON floats that cannot be recovered as a short exact decimal may use continued_fraction approximation so values such as one tenth still land on the familiar one over ten when precision allows. Large numerators or denominators that exceed safe JSON integers are emitted as decimal strings so exactness is preserved without floating-point drift. Missing value, pure letters, and malformed fragments all fail with invalid_input mentioning that the input was non-numeric or incomplete.

API usage, pricing, classroom workflows, and practical limits

Send a JSON body with the required value field set to a decimal string or number, then read numerator, denominator, and fraction from the result. Use the prepaid API when a tutoring platform, coding-assessment sandbox, measurement pipeline, or spreadsheet import step needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with scientific-notation or base-conversion tools when the next step is reformatting rather than rational reduction.