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
-83
-9π
0
40
\frac{10}{7}

Explanation:

Step1: Recall number - set definitions

Whole numbers are non - negative integers (0, 1, 2, …). Integers are whole numbers and their negatives (…, - 2, - 1, 0, 1, 2, …). Rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$. Irrational numbers cannot be written as a fraction.

Step2: Analyze $\frac{10}{7}$

Since $\frac{10}{7}$ is a fraction where 10 and 7 are integers and 7≠0, it is a rational number. It is not an integer (because it is a non - whole fraction), so it goes in the part of the rational numbers circle that is not in the integers circle.

Step3: Analyze 40

40 is a non - negative integer, so it is a whole number. Since whole numbers are a subset of integers and integers are a subset of rational numbers, 40 goes in the whole numbers circle (which is inside the integers circle, which is inside the rational numbers circle).

Step4: Analyze $-9\pi$

Since $\pi$ is an irrational number, $- 9\pi$ is also irrational. So it goes in the irrational numbers circle.

Answer:

Place $\frac{10}{7}$ in the part of the rational numbers circle that is not in the integers circle. Place 40 in the whole numbers circle (inside the integers circle, inside the rational numbers circle). Place $-9\pi$ in the irrational numbers circle.