Calculator Form
Formula Used
1) Reduce the fraction: n/d → n′/d′ where gcd(n, d) removes common factors.
2) Termination rule: a fraction has a terminating decimal only when the reduced denominator can be written as 2a × 5b.
3) Minimum decimal places: m = max(a, b).
4) Decimal value: use long division, or compute n′ × 10m / d′ when the denominator is terminating.
How to Use This Calculator
Enter the numerator and denominator from your fraction.
Choose how many decimal digits you want in the preview.
Set the long division step limit to inspect the decimal process.
Click the calculate button to show the result section above the form.
Review the reduced fraction, factorization, exact decimal, and termination decision.
Use the CSV and PDF buttons to export the displayed result.
Example Data Table
| Input Fraction | Reduced Fraction | Decimal Form | Terminates? | Minimum Decimal Places |
|---|---|---|---|---|
| 1/8 | 1/8 | 0.125 | Yes | 3 |
| 7/20 | 7/20 | 0.35 | Yes | 2 |
| 13/40 | 13/40 | 0.325 | Yes | 3 |
| 5/12 | 5/12 | 0.416666… | No | — |
| 9/125 | 9/125 | 0.072 | Yes | 3 |
FAQs
1) What makes a decimal terminate?
A decimal terminates when the reduced denominator contains no prime factors except 2 and 5. Any other prime factor causes the decimal expansion to continue forever with repeating digits.
2) Why does the calculator reduce the fraction first?
Reduction removes shared factors and reveals the true denominator that controls decimal behavior. A non-reduced fraction can hide the correct answer, so simplification is essential before checking termination.
3) What does minimum decimal places mean?
It is the smallest number of digits needed after the decimal point to write the exact terminating value. The calculator finds it from the largest power of 2 or 5 in the reduced denominator.
4) Why do some results show a preview with dots?
The dots indicate the decimal keeps going beyond the chosen preview length. This happens when the fraction is repeating or when the preview was limited to a certain number of digits.
5) Can negative fractions terminate?
Yes. The sign does not affect termination. Only the prime factors of the reduced denominator matter, so negative fractions follow the same rule as positive fractions.
6) What does the remaining factor show?
The remaining factor is what stays in the reduced denominator after removing all 2s and 5s. If it becomes 1, the decimal terminates. Otherwise, the decimal repeats.
7) Is the exact decimal always shown?
The exact decimal is shown when the fraction terminates. For repeating decimals, the calculator gives a practical preview instead, because the full decimal expansion never ends.
8) What is the graph useful for?
The graph highlights how many 2s, 5s, and other factors remain in the reduced denominator. It gives a quick visual explanation for why a decimal terminates or repeats.