Question

Changing an infinite decimal to a fraction
.577777

Answer 1

`x=0.5777...\ \ \ |multiply\ both\ sides\ by\ 10\\\\10x=5.777...\ \ \ \ |multiply\ both\ sides\ by\ 10\\\\100x=57.777...\\\\make\ a\ difference\ 100x-10x:\\\\90x=57.777...-5.777...\\\\90x=52\ \ \ \ |divide\ both\ sides\ by\ 90\\\\x=(52)/(90)\\\\x=(26)/(45)\\\\\boxed{0.5777...=(26)/(45)}`