Question

Find one irrational number between 0.2101 and 0.2222 . . . 

Answer 1

Let, a = 0.2101
 And, b = 0.2222...
We observe that in 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 numbers
 x = 0.211011001100011....
We find that
 a < x < b
 Hence, x is required an irrational number.