Answer
A decimal number with nonterminating decimals can be expressed in the form of integers with the help of a technique thatinvolves solving a one-step equation.
The decimal number \[0.\overline{9}\] can be expressed as a quotient of integer as follows:
Let \[n\]be equal to the repeating decimal:
\[\begin{align}
& n=0.9999 \\
& 10n=10(0.9999) \\
& 10n=9.9999
\end{align}\]
This is further solved as:
\[\begin{align}
& 10n-n=9.9999-0.9999 \\
& 9n=9 \\
& n=1
\end{align}\]
Thus, \[n=1\] and also \[n=0.\overline{9}\], which gives \[0.\overline{9}=1\].
