Question

question
determine if 0.27322370013414... is rational or irrational and give a reason for your answer.
answer attempt 1 out of 3
the number 0.27322370013414... is because

Explanation:

Step1: Recall rational/irrational definitions

A rational number can be expressed as a fraction $\frac{p}{q}$ (where $p,q$ are integers, $q
eq0$) or has a terminating/repeating decimal. An irrational number has a non - repeating, non - terminating decimal.

Step2: Analyze the given decimal

The decimal $0.27322370013414...$ has a non - repeating and non - terminating decimal expansion (no pattern of digits repeats indefinitely).

Answer:

The number $0.27322370013414...$ is irrational because its decimal expansion is non - repeating and non - terminating (and thus it cannot be expressed as a fraction of two integers).