Question:
Write the value of $2 . \overline{134}$ in the form of a simple fraction.
Solution:
Let, x=2.134134134… …(i)
Multiplying this equation by 1000 on both the sides so that repetitive terms cancel out and we get:
1000x=2134.134134134… …(ii)
Equation (ii)-(i),
⇒ 1000x-x=2134.134134134-2.134134134=2132
⇒ 999x=2132
$\Rightarrow \mathrm{X}=\frac{2132}{999}$
$2 . \overline{134}=\frac{2132}{999}$
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