Sets of numbers
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Express \({\rm{0}}{\rm{.1\dot 2\dot 3}}\) in the simplest rational form
\begin{align}
&\begin{aligned}
\text { Let } x & =0.02 \dot{3}\ldots (1) \\
100 x & =2.3 \dot{2}\dot{3}\ldots (2)
\end{aligned}\\
&(2) -(1)\\
&99 x =2.3 \rightarrow x=\frac{2.3}{99}=\frac{23}{990}\\
&\begin{aligned}
0.1\dot{2}\dot{3} & =0.1+0.0\dot{2}\dot{3} \\
& =\frac{1}{10}+\frac{23}{990} \\
& =\frac{99}{990}+\frac{23}{990} \\
& =\frac{61}{495}
\end{aligned}
\end{align}
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