Repeating Decimal to Fraction Calculator
Convert any repeating decimal (like 0.333…, 0.1(6), or 0.142857142857…) into an exact fraction. Shows step‑by‑step solution and simplifies automatically.
Step 1: Enter Repeating Decimal
Understanding repeating decimals
A repeating decimal has digits that repeat forever. For example, 0.333… = 1/3, 0.1(6) = 1/6, 0.(142857) = 1/7. Our calculator finds the exact fraction.
Step 2: Conversion Options
How the conversion works
We separate non‑repeating and repeating parts, then use the formula: (non‑repeating×(10r‑1) + repeating) / (10n×(10r‑1)). Then simplify.
Fraction Result
Exact Fraction
Common Repeating Decimals and Their Fractions
| Decimal | Repeating Pattern | Fraction |
|---|
How to Convert Repeating Decimals to Fractions
General method
Let x be the decimal. Multiply by 10n to move the non‑repeating part, then subtract to eliminate the repeating tail. Solve for x.
Example: 0.1(6) = 0.1666…
Let x = 0.1666… → 10x = 1.666…, 100x = 16.666… → 100x‑10x = 15 → 90x = 15 → x = 15/90 = 1/6.
Formula
For decimal 0.N(R) where N has n digits, R has r digits:
Fraction = (N·(10r‑1) + R) / (10n·(10r‑1))
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