Fraction to decimal expand

fraction-to-decimal-expand · version 1.0.0 · Money & pricing · free, no key needed

Expand an integer fraction into its exact decimal with the minimal repeating block marked, e.g. 1/7 as 0.(142857).

Use when you need to: convert fraction to repeating decimal · what is 1/7 as a decimal · find the repeating block of a fraction.

Decide before calling

Read the versioned contract and the supported scope below. Reuse fraction-to-decimal-expand@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use fraction-to-decimal-expand@1.0.0 for convert fraction to repeating decimal. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• convert fraction to repeating decimal
• what is 1/7 as a decimal
• find the repeating block of a fraction
• period length of 1/97
• does this fraction terminate or repeat
• long division of a fraction to decimal digits
• non repeating prefix and repeating part of n over d
• expand a fraction with recurring digits

Not supported

• converting decimals or repeating decimals to fractions
• rounding a fraction to a fixed number of places
• mixed numbers, continued fractions or percentages
• fractions with more than 40 digit integers

Behavior

• numerator and denominator are decimal integer strings matching ^-?(0|[1-9][0-9]*)$ with at most 40 digits. A JSON number, a fraction sign, a plus sign, leading zeros, a point, whitespace or more than 40 digits is invalid_input (this is invalid_input, not limit_exceeded, even for a very long digit string).
• denominator 0 -> not_computable with details.reason "division_by_zero", including 0/0. This is checked after all field validation.
• Reduce the fraction to lowest terms first. Only the reduced denominator matters: 24027/56063 is 3/7 and expands as 0.(428571); 8009/16018 is 1/2 and expands as 0.5.
• The sign is negative exactly when numerator and denominator have different signs and the numerator is not zero. Zero has no sign: 0/5, -0/5 and 0/-5 give "0" with negative false. -3/-6 is +0.5.
• The reduced denominator is 2^a * 5^b * m with gcd(m,10) = 1. The non-repeating prefix has max(a,b) digits; the repeating block has length equal to the multiplicative order of 10 modulo m (0 when m = 1). 1/28 = 0.03(571428): prefix "03" (2 digits from 4 = 2^2), block of 6 (order of 10 mod 7).
• Standard long division with remainder tracking: the block starts at the first position whose remainder recurs. The block is the minimal period, never a multiple of it, and never the block "0" or "9". 1/3 is 0.(3), never 0.(33) and never 0.333; 1/2 is 0.5, never 0.5(0) or 0.4(9).
• notation is "[-]" + integer_part, then, when there is a non-empty prefix or block, "." + non_repeating + "(" + repeating + ")" (the parenthesised part only when repeating is non-empty). An integer result has no point: 10/2 gives "5", -10/2 gives "-5". Exactly: 1/6 gives "0.1(6)"; 22/7 gives "3.(142857)"; 1/8 gives "0.125".
• integer_part is floor(|n|/d) as a digit string without sign or leading zeros ("0" when |n| < d). period_length is the length of repeating (0 when terminating). terminating is true iff repeating is empty.
• Period limit: a reduced denominator whose period exceeds 2000 digits -> limit_exceeded, checked after the division-by-zero check and after reduction. A period of exactly 2000 succeeds (1/16001 has period 2000; 1/8009 has period 2002 and is rejected). The check depends only on the period, not on the size of the prefix or numerator.
• Validation order: input not an object; unknown field; missing field; field types and integer grammar and digit limits; then division_by_zero; then the period limit.

Input

• numerator (string, required): min length 1; max length 41; pattern ^-?(0|[1-9][0-9]*)$; Integer numerator as a decimal integer string, at most 40 digits.
• denominator (string, required): min length 1; max length 41; pattern ^-?(0|[1-9][0-9]*)$; Integer denominator as a decimal integer string, at most 40 digits; zero -> not_computable.

Output

• notation (string, required): min length 1; max length 2300; Canonical text: [-]int, then [.non_repeating] and, when the expansion repeats, (repeating) in parentheses.
• integer_part (string, required): min length 1; max length 40; Digits before the point, without sign.
• non_repeating (string, required): max length 140; Fraction digits before the repeating block; may be empty.
• repeating (string, required): max length 2000; The repeating block; empty when the expansion terminates.
• period_length (integer, required): min 0; max 2000; Length of the repeating block; 0 when the expansion terminates.
• terminating (boolean, required): true when the expansion terminates (no repeating block).
• negative (boolean, required): true when the fraction is below zero.

Limits

• max integer digits: 40
• max period: 2000
• max non repeating digits: 132

Example

Request input:

{
  "numerator": "1",
  "denominator": "7"
}

Response:

{
  "result": {
    "notation": "0.(142857)",
    "integer_part": "0",
    "non_repeating": "",
    "repeating": "142857",
    "period_length": 6,
    "terminating": false,
    "negative": false
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "fraction-to-decimal-expand",
  "version": "1.0.0",
  "input": {
    "numerator": "1",
    "denominator": "7"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/fraction-to-decimal-expand/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"numerator":"1","denominator":"7"}'

The machine-readable contract is at /v1/tools/fraction-to-decimal-expand/versions/1.0.0.

CLI

node cli.mjs run fraction-to-decimal-expand 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

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