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
numbers
-3.\overline{8}
4
-13
\frac{9}{8}
0

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 $b
eq0$.

Step2: Place -3.8

-3.8 is a rational number since it can be written as $-\frac{38}{10}=-\frac{19}{5}$, but it is not an integer. So it goes in the part of the rational - numbers set that is outside the integers set.

Step3: Place 4

4 is a whole number (since it is non - negative and an integer), so it goes in the intersection of the whole - numbers and integers sets.

Step4: Place -13

-13 is an integer but not a whole number (because it is negative), so it goes in the part of the integers set that is outside the whole - numbers set.

Step5: Place 0

0 is a whole number and an integer, so it goes in the intersection of the whole - numbers and integers sets.

Step6: Place $\frac{9}{8}$

$\frac{9}{8}$ is a rational number since it is a fraction, but it is not an integer. So it goes in the part of the rational - numbers set that is outside the integers set.

Answer:

-3.8 and $\frac{9}{8}$ go in the part of the rational - numbers set that is outside the integers set. 4 and 0 go in the intersection of the whole - numbers and integers sets. -13 goes in the part of the integers set that is outside the whole - numbers set.