Infinite Decimal Basics

$1÷3=0.\overline{3}$

$3×3=9\Rightarrow0.\overline{3}×3=0.\overline{9}=1$

$\color{#20A900}\boxed{1=0.\overline{9}}$

$\begin{aligned} x&= 0.\overline{99} &\ldots (1) \\ 10x&= 9.\overline{99} &\ldots (2) \end{aligned}$

$(1) - (2) \implies 9x = 9 \implies x =1$

Hence both are equal

First we find the value of 0.999...

0.999...=x 9.999...=10x

Subtracting gives us 9=9x

Solving gives us 1=x

1=1, so they are $\boxed{Equal}$