Calculus with Applications (10th Edition)

$\frac{2}{11}$
The repeating decimal 0.18181818 . . . can be expressed as the infinite geometric series: $0.1818181818...=0.18+0.18(\frac{1}{100})+0.18(\frac{1}{100})^{2}+0.18(\frac{1}{100})^{3}...$ $a=0.18$ $r=\frac{1}{100}$ $\Sigma=\frac{0.18}{1-\frac{1}{100}}=\frac{2}{11}$ and $\frac{2}{11}$ is also $0.1818181818...$