Question

drag each number to the correct location on the table. classify the real numbers as rational or irrational numbers. 5.012121212... √1,000 ∛30 -5/350 0.01562138411... √400 rational numbers irrational numbers

Explanation:

Step1: Recall definitions

A rational number is a number that can be expressed as $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. It includes terminating decimals, repeating decimals, integers, fractions, and square roots of perfect squares. An irrational number is a non - repeating, non - terminating decimal and square roots of non - perfect squares, cube roots of non - perfect cubes etc.

Step2: Analyze each number

• For $5.012121212\cdots$: It is a repeating decimal (the "12" repeats), so it can be expressed as a fraction. So it is rational.
• For $\sqrt{1000}$: $1000 = 10\times10\times10=10^{3}$, $\sqrt{1000}=\sqrt{10^{2}\times10} = 10\sqrt{10}$, and $\sqrt{10}$ is irrational, so $\sqrt{1000}$ is irrational.
• For $\sqrt[3]{30}$: 30 is not a perfect cube, so $\sqrt[3]{30}$ is irrational.
• For $-\frac{5}{350}=-\frac{1}{70}$, it is a fraction of two integers, so it is rational.
• For $0.01562138411\cdots$: It is a non - repeating, non - terminating decimal, so it is irrational.
• For $\sqrt{400}$: $\sqrt{400} = 20$, which is an integer (and can be written as $\frac{20}{1}$), so it is rational.

Answer:

Rational Numbers:

$5.012121212\cdots$, $-\frac{5}{350}$, $\sqrt{400}$

Irrational Numbers:

$\sqrt{1000}$, $\sqrt[3]{30}$, $0.01562138411\cdots$