Question

The value of 1.999. in the form of $\frac{m}{n}$, where m and n are integers and n ≠ 0, is _______.

Answer 1

$$\begin{gathered} \mathrm{Let}x=1.999........\left(1\right) \\ \mathrm{Multiply}\left(1\right)\mathrm{by}10\mathrm{on}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ 10x=19.999........\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 10x-x=19.999....-1.999.... \\ \Rightarrow 9x=18 \\ \Rightarrow x=\frac{18}{9} \\ \Rightarrow x=\frac{2}{1} \end{gathered}$$

Hence, the value of 1.999... in the form of $\frac{m}{n}$, where m and n are integers and n ≠ 0, is $\underline{\frac{2}{1}}$.