Question

build a venn diagram.

• use the names of the sets to label the regions.
• place the numbers in the correct regions.

names of the sets
rational numbers
irrational numbers
integers
whole numbers
numbers
0
40
10

• 9π
• 83

Explanation:

Step1: Recall number - set definitions

Rational numbers can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$. Integers are whole numbers and their negatives. Whole numbers are non - negative integers. Irrational numbers cannot be written as a fraction.

Step2: Classify each number

• $0$: It is a whole number, an integer, and a rational number. So it goes in the intersection of Whole numbers, Integers, and Rational numbers.
• $40$: It is a whole number, an integer, and a rational number. So it goes in the intersection of Whole numbers, Integers, and Rational numbers.
• $\frac{10}{1}$ (which is just 10): It is an integer and a rational number. Since it is positive, it is also a whole number. So it goes in the intersection of Whole numbers, Integers, and Rational numbers.
• $- 83$: It is an integer and a rational number. It is not a whole number. So it goes in the intersection of Integers and Rational numbers but outside of Whole numbers.
• $-9\pi$: Since $\pi$ is irrational, $-9\pi$ is an irrational number. So it goes in the Irrational numbers set.

Answer:

• $0$, $40$, $\frac{10}{1}$ go in the intersection of Whole numbers, Integers, and Rational numbers.
• $-83$ goes in the intersection of Integers and Rational numbers (outside of Whole numbers).
• $-9\pi$ goes in the Irrational numbers set.