Let, a = 0.3010010001
And, b = 0.3030030003...
We observe that in the third decimal place a has digit 1 and b has digit 3, therefore a < b . in the third decimal place a has digit 1. so, if we consider rational and irrational numbers
x = 0.302
y = 0.302002000200002.....
We find that
a < x < b
And, a < y < b
Hence, x and y are required rational and irrational numbers respectively.