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Terminating Decimal Checker — result sheet
Reduce a fraction, factor its denominator, and determine whether its base-10 decimal expansion terminates and how many places it needs.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Reduce p/q to lowest terms. The decimal terminates exactly if the reduced denominator is 2^r5^s; when it terminates, the number of decimal places is max(r,s).
The checker exposes the reduction step before applying the 2-and-5 rule. A terminating value is rendered exactly as a finite decimal; a non-terminating value receives a short repeating-expansion preview rather than a false exact decimal.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Numerator — minimum -1000000000; maximum 1000000000
- Denominator — minimum 1; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Numerator | 3 |
| Denominator | 40 |
3/40 reduces to 3/40 = 0.075; the denominator is 2³×5, so the decimal terminates in 3 places.
Assumptions and limits
- The numerator and denominator are whole numbers and the denominator is positive.
- The result is a base-10 decimal; another numeral base would use the prime factors of that base instead.
- The repeating preview is truncated for display and is not an exact representation of the infinite expansion.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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