Question:
Find one irrational number between $0.2101$ and $0.222 \ldots=0 . \overline{2}$.
Solution:
Let
$a=0.2101$
$b=0.2222 \ldots=0 . \overline{2}$
Here a and b are rational numbers .Since a has terminating and b has repeating decimal. We observe that in second decimal place a has 1 and b has 2. So a < b.
Hence one irrational number is $0.220100100010000 \ldots$ lying between $0.2101$ and $0.2222 \ldots$