Description
Return remainingDenominator and terminating when it equals one.
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.
Return remainingDenominator and terminating when it equals one.
When to use this tool
Use Positional Fraction Terminating Prime Support 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 terminating, remainingDenominator. Inspect terminating before interpreting the associated values.
For positive integer denominator and radix in 2..36 repeatedly divide out their gcd until coprime. Return remainingDenominator and terminating when it equals 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 |
|---|---|---|
| terminating | Terminating | Required. Boolean. |
| remainingDenominator | Remaining Denominator | Required. Safe integer. |
{
"input": {
"denominator": 40,
"radix": 10
},
"output": {
"terminating": true,
"remainingDenominator": 1
}
}Limitations and assumptions
- The conclusion applies to a unit fraction or a rational already reduced to this denominator. The tool does not cancel a numerator, determine a cycle length, or render expansion digits.
- 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
- Positional Digit Carry Single Column
For radix in 2..256, left and right digits within zero through radix-1, and incoming zero or one return digit=(left+right+incoming) modulo radix and carry=floor(sum/radix).
- Continued Fraction Convergent Determinant
Parse exact decimal integers p,previousP,q,previousQ and return determinant=p*previousQ-previousP*q as text, with unimodular=true exactly for determinant +/-1.