Question

solve the problems below. be sure to show your thinking.

1. the following set represents a set of rational numbers:

{-12.6, $\frac{11}{15}$, ___, 0}
which could be the missing value in the set?
a. $8\pi$ b. $\sqrt{196}$ c. 14.32641... d. $\sqrt{105}$

Explanation:

Step1: Recall definition of rational numbers

A rational number can be written as a fraction $\frac{a}{b}$ where $a,b$ are integers and $b
eq0$, or as a terminating or repeating decimal.

Step2: Analyze option A

$8\pi$ is an irrational number since $\pi$ is irrational. So $8\pi$ is not rational.

Step3: Analyze option B

$\sqrt{196} = 14$, and $14=\frac{14}{1}$, which is a rational number.

Step4: Analyze option C

$14.32641...$ is a non - terminating non - repeating decimal, so it is irrational.

Step5: Analyze option D

$\sqrt{105}$ is an irrational number because 105 is not a perfect square.

Answer:

B. $\sqrt{196}$