Let, a = 0.1 = 0.10

And, b = 0.12

We observe that in the second decimal place a has digit 0 and b has digit 2, Therefore

a < b .So, if we consider irrational numbers

x = 0.11011001100011...

y = 0.111011110111110...

We find that,

a < x < y < b

Hence, x and y are required irrational numbers.