Answer: The given number is NOT rational.
Step-by-step explanation: We are given to check whether the number 0.12112111211112 . . . a rational number or not.
We know that
if the digits after the decimal in a number are either repeating or terminating, then the number is rational.
The given number is

We can see that the digits after the decimal are neither repeating nor terminating.
Therefore, the given number is NOT rational.