jmc

We have $$0.\overline{73}=\frac{73}{100}+\frac{73}{10000}+\frac{73}{1000000}+\cdots .$$This infinite geometric series has first term $73/100$ and common ratio $1/100$, so we have $$0.\overline{73}=\frac{73/100}{1-1/100}=\boxed{\frac{73}{99}}.$$