Repeating Decimal to Fraction Calculator
Convert repeating decimals such as 0.(3), 0.1(6), and 1.2(45) to fractions in lowest terms with exact steps.
Examples:
Convert a repeating decimal to a fraction
In US search results, the common wording is repeating decimal to fraction calculator. The tool accepts parenthesis notation such as 0.(3), 0.1(6), and 1.2(45).
A repeating block with one digit uses denominator 9; two repeating digits use 99, and so on.
Here A is the non-repeating block with m digits, and B is the repeating block with n digits.
Repeating decimal examples
| Repeating decimal | Fraction | Notes |
|---|---|---|
| 0.(3) | 1/3 | one repeating digit |
| 0.(6) | 2/3 | one repeating digit |
| 0.1(6) | 1/6 | one non-repeating digit before the repeat |
| 0.(142857) | 1/7 | six repeating digits |
| 1.2(45) | 137/110 | whole part plus repeating block |
Frequently Asked Questions
Sources and References
- Repeating Decimal to Fraction CalculatorCalculatorSoup
- Repeating Decimal to Fraction CalculatorGood Calculators
- Repeating DecimalWolfram MathWorld
- Repeating DecimalWikipedia
Calculations are based on the listed reference sources. Links open in a new tab.
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