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The simplest for of

Question:
The simplest for of $1 . \overline{6}$ is

(a) $\frac{833}{500}$

(b) $\frac{8}{5}$

(C) $\frac{5}{3}$

(d) none of these

Solution:

Let x = 1.6666666... ...(i)
Multiplying by 10 on both sides, we get:
10x = 16.6666666... ...(ii)
Subtracting (i) from (ii), we get:
9x = 15

$\Rightarrow x=\frac{15}{9}=\frac{5}{3}$

None

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