.135 repeating as a fraction

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22-10-2014
Mathematics

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.135 repeating as a fraction

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Анонимidn Анонимidn · Answer 1 · 2014-10-22T14:56:18-04:00

Анонимidn Анонимidn

22-10-2014

[tex]0.135135135...=0.\overline{135}=0.(135)[/tex]

[tex]x=0.(135)\ \ \ \ |multiply\ both\ sides\ by\ 1000\\\\1000x=135.(135)\\\\1000x-x=135.(135)-0.(135)\\\\999x=135\ \ \ \ \ \ |divide\ both\ sides\ by\ 999\\\\x=\frac{135}{999}\\\\divide\ a\ numerator\ and\ a\ denominator\ by\ 27\\\\x=\frac{5}{37}[/tex]

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