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

 (iii)     0.\overline{001}

Answers (1)

Let x = 0.\overline{001}= 0.001001....             -(i)

Now, multiply by 1000 on both sides

1000x= 1.001001...

\Rightarrow 1000x = 1 + x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(using \ (i))

\Rightarrow 999x = 1

\Rightarrow x = \frac{1}{999}

Therefore,  \frac{p}{q}  form of  0.\overline{001}  is  \frac{1}{999}

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