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Fed [463]
3 years ago
8

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

Mathematics
1 answer:
Vladimir [108]3 years ago
7 0
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}}
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