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

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16-10-2014
Mathematics

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

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Анонимidn Анонимidn · Answer 1 · 2014-10-16T08:37:14-04:00

[tex]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}}[/tex]

[tex]So...\ we\ have\ answer:\\\\\boxed{5.764764764...=\frac{5759}{999}}[/tex]

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