Find two irrational numbers lying between 0.1 and 0.12.

Let 

$a=0.1$

$b=0.12$

Here a and b are rational number. So we observe that in first decimal place a and b have same digit. So a < b.

Hence two irrational numbers are $0.1010010001 \ldots$ and $0.11010010001 \ldots$ lying between $0.1$ and $0.12$.