Question

Find one irrational number between 0.2101 and 0.222... = `0.bar2`

Answer 1

Let 

a = 0.2101

b = 0.2222... = `0.bar2`

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... lying between 0.2101 and 0.2222...