Question

Convert 5.764764764... to a rational expression in the form of a/b where b ≠ 0.

Answer 1

$5.764764764....=5.(764)-in\ European\ mathematics\\\\5.764764764....=5.\overline{764}-in\ US\ mathematics\\\\subtitute:\\\\x=5.(764)\ \ \ \ |multiply\ both\ sides\ by\ 1000\\\\1000x=5764.(764)\\\\ let's\ make\ a\ difference\ 1000x-x\ therefore\ we\ have\ the\ equation:\\\\1000x-x=5764.(764)-5.(764)\\\\999x=5759\ \ \ \ \ |divide\ both\ sides\ by\ 999\\\\\boxed{x=\frac{5759}{999}}$

$So...\ we\ have\ answer:\\\\\boxed{5.764764764...=\frac{5759}{999}}$