Question

Find a rational number and an irrational number between:

$a=0.101001000100001...$ and $b=0.1001000100001...$

Answer 1

Let $a=0.101001000100001...$ and $b=0.1001000100001...$.

Here a and b are non-terminating and non-repeating numbers and $a>b$

Hence the rational number between $0.101001000100001...$ and $0.1001000100001...$ is $c=0.101$.

Here c is terminating and $c<b<a$

Hence the irrational number between $0.101$ and $0.1001000100001...$ is $d=0.1002000100001...$