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 = 0.530535305353530...
We find that a < x < y < b
Hence, x and y are required irrational numbers.