Built and fact-checked by the DocNectar team — see our editorial standards
Key Features
Instant Calculation
Get accurate results in real time with our optimized algorithm.
Mobile Friendly
Fully responsive design. Works on all devices & screen sizes.
Privacy Focused
Your data stays on your device. We don't store any inputs.
100% Free
No hidden costs. This tool is completely free forever.
Whether a fraction's decimal form terminates (ends) or repeats forever depends entirely on the prime factors of its denominator once fully reduced. This tool checks any fraction and explains the reasoning using its denominator's prime factorization.
How it works
The fraction is first reduced to lowest terms, then its denominator is factored into primes. If the only prime factors are 2 and/or 5, the decimal terminates; if any other prime factor is present, the decimal repeats forever.
- Enter numerator.
- Enter denominator.
- Click Calculate to see your results.
Examples
A terminating fraction
7/20 reduces to itself (already lowest terms), and 20 = 2² × 5 — only 2s and 5s, so 7/20 = 0.35 terminates.
A repeating fraction
1/3 has denominator 3, which is a prime factor other than 2 or 5, so 1/3 = 0.333... repeats forever.
Who should use it
- Number theory and fraction/decimal coursework.
- Quickly checking whether a fraction will produce a "clean" decimal before converting.
Industry applications
- Mathematics education (number theory)
Advantages
- Shows the full prime factorization of the reduced denominator.
- Explains the underlying base-10 reasoning, not just a yes/no answer.
Limitations
- Only determines termination vs. repetition — does not calculate the specific repeating digit pattern for repeating decimals.
Common mistakes to avoid
- Applying the 2-and-5 rule to the original, unreduced denominator instead of reducing the fraction first.
Best practices
- Always fully reduce a fraction before checking its denominator's prime factors for the terminating-decimal rule.
Tips
- A quick shortcut: if the reduced denominator is a power of 2, a power of 5, or a product of only those two primes, the decimal will terminate — otherwise it repeats.