Question

Convert 8.132132132 … to a rational expression in the form of a over b, where b ≠ 0.

Answer 1

$8.13213213213232....=8+\sum_{i=1}^{\infty}\frac{132}{10^{3i}}=8+\frac{\frac{132}{10^3}}{1-\frac{1}{10^3}}=8+\frac{132}{999}=\frac{8124}{999}$