Question

Express $\mathrm{0.9999.......}$ in the $\frac{p}{q}$ form

Answer 1

Let x=0.99999….

Then, 10x=0.99999….x10

=9.99999…

=9+0.99999….

Since x=0.99999…, we can write:

10x=9+x

$\Rightarrow 10x-x=9$

$\Rightarrow 9x=9$

$\Rightarrow x=1$

This means 0.99999.,..=1 answer