Repeating Decimal Calculator
Convert a repeating decimal block to an exact fraction, or find a fraction’s terminating prefix and complete repeating cycle.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Multiply a repeating block by a power of ten to align its repetitions, then subtract to cancel the infinite tail. In the other direction, long division repeats when the same nonzero remainder occurs again.
W.A(B) = W + A/10^k + B/[10^k(10^r−1)]
Worked example
0.1(6)=1/10+6/90=1/6. The fraction1/7 gives0.(142857). Parentheses mark the repeating block.
Assumptions and input details
The integer part supplies the sign for the entire decimal, so −0 with block3 means−0.(3). Decimal input allows up to six digits in each block. Fraction input accepts at most50 characters, a numerator within±1e12 and reduced denominator≤10000; the displayed cycle is complete, not guessed from a rounded decimal.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Integer and fraction results are exact within the documented limits. Radical decimal values and plotted interval positions are approximate.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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