Find two irrational numbers between

Let 

$a=0.5$

$b=0.55$

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 $0.510100100010000 \ldots$ and $0.5202002000200002 \ldots$ lying between $0.5$ and $0.55$.