Express the recurring decimal
$0.125 125 125....$ as a rational number.

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Solution

Let $x = 0 \cdot 125125125$
$∴ 1000 x = 125.125125125...$
Subtract $999 x = 125 \cdot 0000000 = 125$
$∴ x = \frac{125}{999}$

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