The simplest form of
Question:

The simplest form of $0.12 \overline{3}$ is

(a) $\frac{41}{330}$

(b) $\frac{37}{330}$

(c) $\frac{41}{333}$

(d) none of these

 

Solution:

(d) none of these
Let x = 0.12333333333…         …(i)
Multiplying by 100 on both sides, we get:
100x = 12.33333333…             …(ii)
Multiplying by 10 on both sides, we get:
1000x = 123.33333333…         …(iii)
Subtracting (ii) from (iii), we get:
900x = 111

$\Rightarrow x=\frac{111}{900}$

 

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