Question:
Express the recurring decimal 0.125125125 …. $=0 . \overline{125}$ as a rational number.
Solution:
Let, x=0.125125125… …(i)
Multiplying this equation by 1000 on both the sides so that repetitive terms cancel out and we get:
1000x=125.125125125… …(ii)
Equation (ii)-(i),
⇒ 1000x-x=125.125125125-0.125125125=125
⇒ 999x=125
$\Rightarrow \mathrm{X}=\frac{125}{999}$
$0 . \overline{125}=\frac{125}{999}$
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