# 4.  Express 0.99999 .... in the form $\frac{p}{q}$ . Are you surprised by your answer?

G Gautam harsolia

Let $x = 0.\overline{9}= 0.9999....$             -(i)

Now, multiply by 10 on both sides

$10x= 9.999....$

$\Rightarrow 10x = 9 + x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(using \ (i))$

$\Rightarrow 9x = 9$

$\Rightarrow x = \frac{9}{9} = 1$

Therefore,  $\frac{p}{q}$  form of  $0.999....$  is  1

The difference between 1 and 0.999999 is o.000001 which is almost negligible.

Therefore, 0.999 is too much closer to 1. Hence, we can write 0.999999.... as 1

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