Question

Find two irrational numbers between 0.5 and 0.55.

Answer 1

Let a = 0.5 = 0.50 

And, b = 0.55 

We observe that in the second decimal place a has digit 0 and b has digit 5. Therefore a < b. So, if we consider irrational numbers 

x = 0.51051005100051… 

y = 0.5305343055353530… 

We find that, 

a < x < y < b 

Hence, x and y are required irrational numbers.