Question

Find a rational number and also an irrational number lying between the numbers 0.3030030003... and 0.3010010001...

Answer 1

Let 

a = 0.3030030003...

b = 0.3010010001...

Here decimal representation of a and b are non-terminating and non-repeating. So a and b are irrational numbers. We observe that in first two decimal place of a and b have the same digit but digit in the third place of their decimal representation is distinct.

Therefore, a > b.

Hence one rational number is 0.3011 lying between 0.3030030003... and 0.3010010001...

And irrational number is 0.3020200200020000... lying between 0.3030030003... and 0.3010010001...