Question

question
determine if 0.0145418792336334... is rational or irrational and give a reason for answer.
answer attempt 1 out of 2
the number 0.0145418792336334... is because
irrational
rational

Explanation:

Step1: Recall definitions

A rational number can be expressed as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$, and its decimal expansion is either terminating or repeating. An irrational number has a non - repeating, non - terminating decimal expansion.

Step2: Analyze the given number

The number $0.0145418792336334\ldots$ has a decimal expansion that does not show any repeating pattern and it is non - terminating (the "..." indicates it goes on without end). Since it is non - repeating and non - terminating, it cannot be expressed as a fraction of two integers.

Answer:

The number $0.0145418792336334\ldots$ is irrational because its decimal expansion is non - repeating and non - terminating, so it cannot be written as a fraction of two integers.