Question

answer the question correctly to continue! which of the following sets only contains rational numbers? 2, 0.5, - 3, 7/4; √2, 0.5, 3

Explanation:

Step1: Recall rational number definition

A rational number can be written as $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. Integers and terminating or repeating decimals are rational.

Step2: Analyze first set

The set $\{2, 0.5,-3,\frac{7}{4}\}$: 2 is an integer (so rational), $0.5=\frac{1}{2}$ is rational, - 3 is an integer (so rational), and $\frac{7}{4}$ is a fraction (so rational).

Step3: Analyze second set

The set $\{\sqrt{2},0.5,3\}$: $\sqrt{2}$ is an irrational number as it cannot be written as a fraction of two integers, while 0.5 and 3 are rational.

Answer:

The set $\{2, 0.5,-3,\frac{7}{4}\}$