Find a rational number and also irrational number lying between the numbers 0.3030030003…..and 0.3010010001….
Let a = 0.3010010001….
And, b = 0.3030030003…..
We observe that the second 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.