Let x = 0.99999..... ......(a)

We need to multiply by 10 on both sides, we get

10x = 9.9999.... ........(b)

**Subtract the equation (a) from (b), to get**

\(\cfrac{\begin{matrix}10\mathrm x=9.99999....\\-\mathrm x = 0.99999....\end{matrix}}{9\mathrm x=9}\)

9x = 9 as x = \( \frac{9}{9}\) or x = 1.

Therefore, on converting 0.99999..... \( =\frac{1}{1}\) which is in the \( \frac{p}{q}\) form,

Yes, at a glance we are surprised at our answer.

But the answer makes sense when we observe that 0.9999……… goes on forever.

So, there is no gap between 1 and 0.9999……. and hence they are equal.

Answered by Shivani Kumari | 2 years agoVisualise the representation of \( 5.3\overline{7}\) on the number line upto 5 decimal places, that is upto 5.37777.

Visualise 2.665 on the number line, using successive magnification.

Find whether the following statements are true or false:

**(i) **Every real number is either rational or irrational.

**(ii)** π is an irrational number.

**(iii)** Irrational numbers cannot be represented by points on the number line.