5. richie says that 2.141441444... is a rational number. elsa disagrees. a. who is correct? b. what is the…

5. richie says that 2.141441444... is a rational number. elsa disagrees. a. who is correct? b. what is the likely cause of the error?

5. richie says that 2.141441444... is a rational number. elsa disagrees. a. who is correct? b. what is the likely cause of the error?

Answer

Explanation:

Step1: Recall definition of rational numbers

A rational number can be written as a fraction $\frac{p}{q}$ where $p,q\in\mathbb{Z}$ and $q\neq0$. A non - repeating and non - terminating decimal is an irrational number. The number 2.141441444... is non - repeating and non - terminating.

Step2: Determine who is correct

Since 2.141441444... is non - repeating and non - terminating, it is an irrational number. So Elsa is correct.

Answer:

a. Elsa is correct. b. The likely cause of the error is a misunderstanding of the definition of rational and irrational numbers. Richie may have thought that just because it has a pattern (but not a repeating pattern) it was rational. In fact, rational numbers have either terminating or repeating decimal expansions.