Express the repeating decimal $0.\overline{61}$ as a fraction in lowest terms.

Step-by-step solution

1. Let $x=0.\overline{61}$.
2. Multiply by $100$ to shift two decimal places: $100x=61.\overline{61}$.
3. Subtract the original $x$ from this equation: $100x-x=61$.
4. Simplify: $99x=61$.
5. Solve for $x$: $x=\frac{61}{99}$.
6. Since $gcd(61,99)=1$, the fraction is already in lowest terms.

Concept tested: Repeating decimal to fraction

Published 4 October 2026 · How this solution was prepared and checked