Question

Rewrite as a simplified fraction 1.5 <-- repeating=?

Answer 1

$1.5555...=1.\overline{5}=1.(5)\\\\x=1.5555...\ \ \ |multiply\ both\ sides\ by\ 10\\10x=15.5555...\\\\10x-x=15.5555...-1.5555...\\9x=14\ \ \ \ |divide\ both\ sides\ by\ 9\\\\x=\frac{14}{9}\\\\\boxed{x=1\frac{5}{9}}$