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3 years ago

5

.135 repeating as a fraction

1 answer:

ladessa [460]3 years ago

3 0

$0.135135135...=0.\overline{135}=0.(135)$

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

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