Question

Rewrite as a simplified fraction 2.16 <-- repeating =?

Answer 1

$x=2.161616...=2.\overline{16}=2.(16)\\\\x=2.161616....\ \ \ \ |multiply\ both\ sides\ by\ 100\\100x=216.161616...\\\\100x-x=216.161616...-2.161616...\\99x=214\ \ \ \ |divide\ both\ sides\ by\ 99\\\\x=\frac{214}{99}\\\\x=\frac{198+16}{99}\\\\x=\frac{198}{99}+\frac{16}{99}\\\\\boxed{x=2\frac{16}{99}}$