Why reduce before checking whether the decimal repeats?
Shared factors can hide the real denominator. For example, 6/12 reduces to 1/2, so it terminates even though the original denominator is 12.
Fraction to Decimal Calculator
Convert a fraction by treating the fraction bar as division, then check the reduced denominator to know whether the decimal ends or repeats.
Convert by dividing, classify by reducing
Decimal behavior depends on the reduced denominator, not necessarily the denominator you typed. After reduction, denominators made only from factors 2 and 5 terminate; every other prime factor repeats.
Read the decimal correctly
- Enter numerator and denominator.
- Reduce the fraction first.
- Divide numerator by denominator.
- Inspect the reduced denominator factors.
- Compare exact and rounded output.
Loading tool...
Division and termination test
The same fraction value can have different-looking denominators before and after reduction.
Division
Reduced fraction
Termination test
Decimal places
Exact check
Practical checks
- A reduced denominator with only 2s and 5s terminates.
- Other prime factors create a repeating decimal.
- A zero denominator is invalid.
- A rounded display may not multiply back exactly.
FAQ
Does a rounded decimal equal the original fraction?
Only if the calculator marks it as exact. A rounded display is an approximation, so multiplying it back by the denominator may not return the original numerator exactly.
