Question

drag and drop each number on the right into the correct, most specific classification.
rational
integers
whole numbers
natural numbers
irrational
$-\frac{2}{3}$ $2.79$ $-7.1$
$12.overline{6}$ $-14$ $-sqrt{36}$
$sqrt{9}$ $pi$ $3\frac{1}{4}$
$192$ $sqrt{24}$ $0$
$\frac{8}{4}$ $-6.overline{05}$ $-sqrt{3}$
$-32$ $-\frac{7}{5}$ $-\frac{20}{2}$
$8$ $1.325...$ $7pi$

Explanation:

Step1: Classify Natural Numbers

Natural numbers are positive counting numbers: $8, 192$

Step2: Classify Whole Numbers

Whole numbers include natural numbers + 0: $8, 192, 0$

Step3: Classify Integers

Integers include whole numbers + negative integers. Simplify $-\sqrt{36}=-6$, $-\frac{20}{2}=-10$: $8, 192, 0, -14, -32, -\sqrt{36}, -\frac{20}{2}$

Step4: Classify Rational Numbers

Rational numbers include integers + fractions/terminating/repeating decimals. Simplify $\frac{8}{4}=2$, $\sqrt{9}=3$: $8, 192, 0, -14, -32, -\sqrt{36}, -\frac{20}{2}, -\frac{2}{3}, 2.79, -7.1, 12.\overline{6}, \sqrt{9}, 3\frac{1}{4}, \frac{8}{4}, -6.\overline{05}, -\frac{7}{5}$

Step5: Classify Irrational Numbers

Irrational numbers are non-terminating/non-repeating decimals: $\pi, \sqrt{24}, -\sqrt{3}, 1.325..., 7\pi$

Answer:

• NATURAL NUMBERS: $8, 192$
• WHOLE NUMBERS: $8, 192, 0$
• INTEGERS: $8, 192, 0, -14, -32, -\sqrt{36}, -\frac{20}{2}$
• RATIONAL: $8, 192, 0, -14, -32, -\sqrt{36}, -\frac{20}{2}, -\frac{2}{3}, 2.79, -7.1, 12.\overline{6}, \sqrt{9}, 3\frac{1}{4}, \frac{8}{4}, -6.\overline{05}, -\frac{7}{5}$
• IRRATIONAL: $\pi, \sqrt{24}, -\sqrt{3}, 1.325..., 7\pi$