Input
Result
Bar notation
Reverse check
The reduced fraction expands back to .
10^k algebra steps
GCD simplification
The result uses exact BigInt integer arithmetic. No floating-point rounding is used to build the fraction.
When to use this page
Use this page when you already know which digits repeat and want the exact fraction. For fraction arithmetic, use the fraction calculator. To reduce an existing fraction, use the fraction simplifier. To see long division steps that create a repeating decimal, use the long division calculator.
FAQ
How do I type the repeating part?
Use parentheses for the repetend, such as 0.1(6) or 0.(142857). You can also choose Last k digits repeat, type a normal decimal such as 0.1666, and set k to 1.
Why does 0.999... become 1?
The algebra gives 9x = 9 for x = 0.(9), so x = 1. The calculator shows this as a normal exact simplification, not as rounding.
What is the difference between a terminating decimal and a repeating decimal?
A terminating decimal has no repeating block and uses a place-value denominator such as 10, 100, or 1000. A repeating decimal subtracts two powers of 10 so the repeating tail cancels.
Are the fractions exact?
Yes. The parser and simplifier use BigInt integer arithmetic, so the fraction is exact. Decimal text is used only for display and for the reverse check.
Can I use bar notation instead of parentheses?
Type the repeated digits in parentheses, then read the result in bar notation. For example, enter 0.1(6) for 0.16 with only the 6 repeating.