Question

Give two rational numbers lying between 0.232332333233332... and 0.212112111211112.

Answer 1

Let 

a = 0.232332333233332...

b = 0.212112111211112...

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 2 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... and 0.212112111211112...