Express $0.00 ¯ ¯¯¯¯¯¯ ¯ 135$ as a fraction.

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Solution

$x = 0.00 ¯ ¯¯¯¯¯¯ ¯ 135$

$x = 0.00135135......$

$100 x = 0.135135.....$ (1)

$100000 x = 135.135135......$ (2)

Subtract (1) from (2),

$100000 x - 100 x = 135$

$99900 x = 135$

$x = \frac{135}{99900}$

$x = \frac{3}{2220}$

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