Question

Classify the following numbers as rational or irrational :

$\left(v\right)1.101001000100001...$

Answer 1

A rational and irrational number.

Any decimal representation that is terminating or non-terminating but repeating of digits after the decimal point will be a rational number.

Any decimal representation that is non-terminating and non-recurring, will be an irrational number.

The given decimal number $1.101001000100001...$ is non-terminating and non-recurring.

Hence, the given number $1.101001000100001...$ is an irrational number.