Question

Find one irrational number between 0.2101 and 0.2222 ….= .\(0.\overline2\).

Answer 1

Let a = 0.2101 

And, b = 0.2222…. 

We observe that the second decimal place a has digit 1 and b has digit 2, therefore, a < b. In the third decimal place a has digit 0. So, if we consider irrational number 

x = 0.211011001100011… 

We find that, 

a < x < b 

Hence, x is required irrational number