3. Express the following in the form \frac{p}{q} , where p and q are integers and q ≠ 0.

(i)      0.\bar{6}

Answers (1)

Let x = 0.\overline6= 0.6666....             -(i)

Now, multiply by 10 on both sides

10x= 6.6666...

\Rightarrow 10x = 6 + x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(using \ (i))

\Rightarrow 9x = 6

\Rightarrow x = \frac{6}{9} = \frac{2}{3}

Therefore,  \frac{p}{q}  form of  0.\bar{6}  is  \frac{2}{3}

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