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How to write -0.7 repeating as a fraction?

1 Answer

5 votes

x=0.\overline{7}\ \ \ \ \ |multiply\ both\ sides\ by\ 10\\\\10x=7.\overline{7}\\\\10x-x=7.\overline{7}-0.\overline{7}\\\\9x=7\ \ \ \ \ |divide\ both\ sides\ by\ 7\\\\x=(7)/(9)\\\\Answer:\boxed{0.\overline{7}=(7)/(9)}



other:\\\\We\ know:0.\overline{1}=(1)/(9)\ then\ 0.\overline{7}=(7)/(9)
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