Certainly most students would agree that \(0.333333... = \frac{1}{3} \text{.}\) So, what about \(0.999999...\text{?}\) Simply follow the pattern above
\begin{align*}
0.999999... & = 0.9 + 0.09 + 0.009 + 0.0009 + ... = 0.9(1 + 0.1 + 0.1^2 + 0.1^3 + ...\\
& = 0.9 \frac{1}{1-0.1} = 0.9 \frac{1}{0.9} = 1
\end{align*}