Give two rational numbers lying between

Let 

$a=0.232332333233332 \ldots$

$b=0.212112111211112 \ldots$

Here the decimal representation of a and b are non-terminating and non-repeating. So we observe that in first decimal place of a and b have the same digit but digit in the second place of their decimal representation are distinct. And the number a has 3 and b has 1. So a > b.

Hence two rational numbers are $0.222,0.221$ lying between $0.232332333233332 \ldots$ and $0.212112111211112 \ldots$