Enter values such as 0.(3), 0.1(6), or 12.34(56) and convert the repeating decimal to a reduced exact fraction.
Convert repeating-decimal notation to an exact reduced fraction with integer-equation steps, gcd reduction and decimal round-trip verification.
Equivalent fraction forms should preserve the same rational value, and number-theory relationships should agree across factors, remainders, GCF, multiples, and prime structure. Use the connected tools to verify rather than relying on an isolated answer.
Use the tool first, then apply these checks to verify the inputs, interpret the result, and hand it off without displacing the primary workflow.
0.1(6) means only the 6 repeats, while 0.(16) means the two-digit block 16 repeats. Moving the parentheses changes the fraction even when the first few decimal digits look similar.
When a decimal has both fixed and repeating digits, the power-of-ten shifts must account for both lengths. The proof workspace is useful because it makes those shifts and the subtraction step visible.
The first numerator and denominator produced by the repeating-decimal identity may share a common factor. Reduce them with a greatest-common-divisor check rather than assuming the unreduced ratio is the simplest exact answer.
Re-expanding the fraction should reproduce the entered repeating pattern, but a rounded decimal display cannot prove equality indefinitely. Keep the reduced fraction and symbolic repeating form as the exact representations. If the repeating block is long, verify the reconstructed decimal over several full cycles so an incorrectly placed parenthesis is easier to detect.
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