Fraction Nearest Integer Tie Policy
Round an exact fraction to a nearest integer with explicit half-even, away-from-zero or positive-infinity tie policy.
Description
Round an exact fraction to a nearest integer with explicit half-even, away-from-zero or positive-infinity tie policy.
Nearest-integer rounding needs an explicit policy when a fraction lies exactly halfway between integers.
When to use this tool
Round an exact fraction to a nearest integer with explicit half-even, away-from-zero or positive-infinity tie policy.
- Prepare the supplied numerator, denominator, ties fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter numerator, denominator, ties. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.integer, result.tie. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Normalize the fraction, compute its mathematical floor and nonnegative remainder, then compare twice the remainder with denominator. On equality use ties even, away from zero or positive infinity according to even, away or positive. Return integer text and a tie flag.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| numerator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| denominator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| ties | ties. | Text; at most 8,192 UTF-16 code units, subject to the grammar above |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.integer | Exact decimal integer text under the operation described above. |
| result.tie | Flag for tie under the exact condition described above. |
{
"input": {
"numerator": "-5",
"denominator": "2",
"ties": "even"
},
"output": {
"result": {
"integer": "-2",
"tie": true
}
}
}Limitations and assumptions
- These policies differ for negative halves. There is no configurable decimal-place rounding or floating-point approximation.
- Numerator and denominator fields use exact decimal integer strings of at most 256 digits with an optional sign. Fractions are reduced with a positive denominator before the stated operation.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Use exact numerator/denominator operations when equality and boundary decisions matter. Convert to a decimal display only with an explicit rounding policy; a rounded display should not replace the exact result.
References
Similar or alternative tools
- Fraction Between Integer Bounds
Check exact rational membership in caller-supplied inclusive integer bounds without decimal approximation.
- Fraction Floor and Remainder
Split an exact rational into mathematical floor and a nonnegative reduced fractional remainder; signed numerators are not truncated toward zero.