Fraction to Decimal Converter
Convert a fraction to its exact decimal, detecting repeating digits and showing them in brackets.
Your inputs
Results
Exact decimal (repeating digits in brackets)
0.(714285)
- Decimal approximation
- 0.714285714286
- Type
- Repeating, period 6
- As a percentage
- 71.428571%
✓Exact calculation — rounded only for display
What this calculator does
Every fraction becomes either a terminating decimal or a repeating one. Long division reveals the repeating cycle exactly.
Formula and method
Long division of numerator by denominator; a remainder that repeats marks the start of the repeating block.
Worked example
Calculated by this tool with its default inputs:
Inputs
- Fraction: 5/7
Results
- Exact decimal (repeating digits in brackets): 0.(714285)
- Decimal approximation: 0.714285714286
- Type: Repeating, period 6
- As a percentage: 71.428571%
How to read the results
A fraction terminates only if its denominator (in lowest terms) has no prime factors other than 2 and 5.
Assumptions and limitations
- Very long periods are truncated after 2,000 digits.
Questions
What does 0.1(6) mean?
0.16666…, with the 6 repeating forever.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 5 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
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