Description
Nonrepeating prefix length for a reduced rational denominator in the supplied radix; numerator must already be coprime.
A positional representation depends on its radix, digit range, sign convention, and treatment of leading zeros. Ordinary bases use digits from zero through radix minus one, while negative and bijective bases have different conversion rules. A single carry, borrow, or denominator step is distinct from formatting a complete number.
Nonrepeating prefix length for a reduced rational denominator in the supplied radix; numerator must already be coprime.
When to use this tool
Use Rational Repetend Pre Period Budget when you need this digit, carry, borrow, sign, width, or denominator component for an explicit radix convention.
How to use the tool and how it works
- Enter denominator, radix. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read prePeriod, remainingDenominator, terminates. Inspect terminates before interpreting the associated values.
For positive integer denominator and radix in 2..36 repeatedly divide the denominator by gcd(denominator,radix) until coprime. Return prePeriod as the iteration count, remainingDenominator, and terminates when the remainder is one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| denominator | Denominator or exact integer denominator text under the stated sign restriction. | Required. Safe integer; minimum 1. |
| radix | Positional base within the explicit stated bound. | Required. Safe integer; minimum 2; maximum 36. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| prePeriod | Number of radix-digit positions needed to remove shared denominator factors. | Required. Safe integer. |
| remainingDenominator | Remaining Denominator | Required. Safe integer. |
| terminates | Terminates | Required. Boolean. |
{
"input": {
"denominator": 12,
"radix": 10
},
"output": {
"prePeriod": 2,
"remainingDenominator": 3,
"terminates": false
}
}Limitations and assumptions
- The rule applies to a unit fraction or an already-reduced rational denominator. It does not cancel an unspecified numerator or calculate the repeating cycle length; prePeriod counts radix positions before the recurring part.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Choose the full conversion or formatting workflow for the intended representation. Keep radix, digit alphabet, leading-zero width, signed-zero handling, and terminating/repeating-fraction assumptions explicit.
References
Similar or alternative tools
- Radix Repeating Cycle Denominator Order
Find the repeating period of 1/denominator after removing factors shared with the radix.
- Positional Fraction Terminating Prime Support
Return remainingDenominator and terminating when it equals one.