Sets of Numbers WS
Name ________________________________
Check each set to which the numbers belong.
R = Real Numbers
Ir. = Irrational Numbers
 Ir. or ~Q = all nonterminating, non-repeating
decimals
Q = Rational Numbers
 Q = {a/b | a and b integers and
b  0}
Z = Integers
 Z = {…, 3, 2, 1, 0, 1,
2,…}
W = Whole Numbers
 W = {0, 1, 2, 3, 4, 5, …}
N = Natural Numbers
 N = {1, 2, 3, 4, 5, …}
Ir.
N
Z
W
The Real Numbers
Complex Numbers
R
Ir.
Q
Z
W
1. – ½
2. 16
3. 
4. – 2
5.
Q
11
Give two examples of each number system.
6. Natural Numbers:
__________
__________
7. Whole Numbers
__________
__________
8. Integers
__________
__________
9. Rational Numbers
__________
__________
10. Irrational Numbers __________
__________
Match each Number System with its correct Set Builder Notation.
11. Natural Numbers _____
a. { 0, 1, 2, 3, ...}
12. Whole Numbers _____
b. { x | x is not rational}
13. Integers _____
c. { 1, 2, 3, 4, 5, ...}
14. Rational Numbers _____
d. { ..., -3, -2, -1, 0, 1, 2, 3, ...}
15. Irrational Numbers _____
e. { a/b | a and b are integers and b is not 0.}
N
Multiple Choice. Choose the correct answer.
16.
2 belongs to which of the following sets?
a. Natural
17.
b. Whole
c. Integer
d. Rational
b. Whole
c. Irrational
d. Rational
Which of the following is NOT rational?
a. ½
20.
d. Rational
What set of numbers did we first learn as children?
a. Natural
19.
c. Irrational
The number 0 belongs to ALL of the following sets EXCEPT ...
a. Natural
18.
b. Whole
b. ¾
c. 
d. –0.123
c. 
d.
Which of the following is rational?
a. 1.123....
b. 0.3
5
True or False. Answer each as true or false.
21.
The number 0 is a Natural Number.
__________
22.
A number can be rational AND irrational.
__________
23.
There are numbers that belong to more than one number system.
__________
24.
All fractions are integers.
__________
25.
There are more irrational numbers than rational numbers.
__________
Higher-Level Thinking Questions. Read and answer each question very carefully.
26.
Give a number that is an integer, but not a whole number.
__________
27.
Give a number that is a rational number, but not an integer.
__________
28.
Give a number that is a natural number, whole number, and integer.
__________
29.
Give a number that is NOT rational.
__________
30.
Give a number that is a whole number, but not a natural number.
__________