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.