Question

classify the numbers as rational or irrational.
-4
0
-4·0
rational
irrational

Explanation:

Step1: Recall Rational Number Definition

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

Step2: Analyze -4

-4 is an integer. It can be written as $\frac{-4}{1}$, so it is rational.

Step3: Analyze 0

0 is an integer. It can be written as $\frac{0}{1}$, so it is rational.

Step4: Analyze -4.0

-4.0 is a terminating decimal (equivalent to -4, an integer). It can be written as $\frac{-4}{1}$, so it is rational.

Step5: Analyze Irrational Category

Irrational numbers cannot be expressed as $\frac{p}{q}$ (e.g., $\pi$, $\sqrt{2}$). None of the given numbers are irrational.

Answer:

rational: -4, 0, -4.0
irrational: (empty, no irrational numbers here)