Question

Express $0.99999.....$ in the form $\frac{p}{q}$. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Answer 1

Solution:-

Let $x=\mathrm{0.99999.....}...\left(1\right)$

Multiplying both sides with $10$, we get

$10x=\mathrm{9.9999......}...\left(2\right)$

Subtracting ${eq}^n\left(1\right)$ from $\left(2\right)$, we have

$10x-x=\mathrm{9.9999...}-\mathrm{0.99999.....}$

$\Rightarrow 9x=9$

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

$\Rightarrow x=1$

Hence $\mathrm{0.99999.....}=1$.