Description
Find the repeating period of 1/denominator after removing factors shared with the radix.
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.
Find the repeating period of 1/denominator after removing factors shared with the radix.
When to use this tool
Use Radix Repeating Cycle Denominator Order 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 period, terminating. Inspect terminating before interpreting the associated values.
For denominator in 1..10000 and radix in 2..36 remove common radix factors. If the remaining denominator is one return period=0 and terminating=true; otherwise iterate radix powers modulo that denominator until one returns, counting the multiplicative order as period.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; maximum 10000. |
| radix | Positional base within the explicit stated bound. | Required. Safe integer; minimum 2; maximum 36. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| period | Period | Required. Safe integer. |
| terminating | Terminating | Required. Boolean. |
{
"input": {
"denominator": 7,
"radix": 10
},
"output": {
"period": 6,
"terminating": false
}
}Limitations and assumptions
- This describes a unit fraction or already-reduced denominator. No numerator cancellation, actual expansion digits, leading nonrepeating length, or denominator above the bounded domain is supported.
- 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
- Rational Repetend Pre Period Budget
Nonrepeating prefix length for a reduced rational denominator in the supplied radix; numerator must already be coprime.
- Positional Fraction Terminating Prime Support
Return remainingDenominator and terminating when it equals one.