Simple repeating
- Input
- 1/3
- Expected output
- 0.3[3]
The digit 3 repeats indefinitely.
fraction to decimal with repeating
Fraction to Decimal — Repeating Decimal Detection
Every fraction a/b has either a terminating or repeating decimal. This tool detects the repeating block.
When does a fraction have a repeating decimal?
- A fraction a/b (in lowest terms) has a terminating decimal if and only if the only prime factors of b are 2 and 5. Otherwise, it repeats.
- 1/4 = 0.25 (terminating, since 4 = 2²). 1/3 = 0.3[3] (repeating, since 3 ≠ 2ⁿ × 5ᵐ).
Examples
Long period
- Input
- 1/7
- Expected output
- 0.[142857]
The block 142857 repeats.
Full tool FAQ
Simplifying means dividing both the numerator and denominator by their Greatest Common Divisor (GCD) until no integer greater than 1 divides both. The resulting fraction is equivalent but in its most reduced form.
Frequently asked questions
Does every fraction have a decimal representation?
Yes. Every rational fraction has either a terminating or repeating decimal.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.