Question

DRAG AND DROP EACH PIECE FROM THE MIDDLE INTO THE CORRECT RED BOX

Answer 1

Step-by-step explanation / Answers:

First, let's define rational and irrational numbers:

Rational. It's any number that can be represented as the ratio of 2 integers.

Irrational. It's any number that can't be represented as the ratio of 2 integers.

Now, using the concepts explained previously, let's classify each number by finding their decimal form:

$12\frac{3}{4} =12+\frac{3}{4} =\frac{48}{4} +\frac{3}{4} =\frac{51}{4}=12.75$, hence, this number is rational.

$-33=\frac{-330}{10}$, hence, this number is rational.

$\sqrt{22}= 4.69041576...$, hence, this number is irrational.

$0.7$(repeating). All repeating numbers are irrational.

13.654.... Since this number isn't shown as a defined exact decimal number, due to the fact that it has ellipsis at the end, it's an irrational number.

$3\pi$. Pi is one of the most known numbers in math, and it's irrational. Hence $3\pi$ is an irrational number.

$4\sqrt{100} =4(10)=40=\frac{400}{10}$, hence, this number is rational.

$-\frac{1}{3}=-0.3333333333...$, hence, this number is irrational.

$\sqrt{200} =14.14213562...$, hence, this number is irrational.

8.462.... Since this number isn't shown as a defined exact decimal number, due to the fact that it has ellipsis at the end, it's an irrational number.

Note.

All natural, integers and whole numbers are rational numbers, because of the reasons explained at the beginning of this answer.

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