Question

find rational numberwhose decimal expansion is 0.322222.........​

Answer 1

     

Let the rational number (the answer) be x.

So that,

$x=0.322222... \\ \\ \Rightarrow\ x=0.3\overline{2}$

$\Rightarrow\ x=0.3\overline{2} \\ \\ \Rightarrow\ 10x=3.\overline{2} \\ \\ \Rightarrow\ 100x=32.\overline{2} \\ \\ \\ \\ \Rightarrow\ 100x-10x=32.\overline{2}-3.\overline{2} \\ \\ \Rightarrow\ 90x=29\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [32.\overline{2}-3.\overline{2}=32-3=29] \\ \\ \Rightarrow\ x=\bold{\frac{29}{90}}$

So, 29/90 is the rational number.

Thank you. :-))