MATH 80/80A UNIT 1.2
SUPPLEMENT
IDENTIFYING NUMBERS
1, 2,3.....
Natural numbers (counting numbers):

3 2 1 0 1 2 3
Natural numbers DO NOT include negative numbers, zero, decimals, and fractions
Whole numbers:0,1, 2,3...

3 2 1 0 1 2 3
Whole numbers are similar to natural numbers, with the exception that it INCLUDES the zero
Integers: ...  3, 2, 1,0,1, 2,3...

3 2 1 0 1 2 3
Integers consist of whole numbers, natural numbers, and ONLY fractions & square roots that
simplify into an integer.
Examples:
6
,
3
36,
0,
1
a
 a and b are integers and b  0
b
Rational numbers consist of natural numbers, whole numbers, integers, and every decimal that
Rational numbers:
either repeats or terminates
Every integer is a rational number since each integer can be written as the quotient of itself and
1:
Examples:
2
2
1
1
 0.5
2
2
 0.6666666...  6
3
1
 0.090909  0.09
11
5
 1.25
4
Irrational numbers: An irrational number is a decimal that NEITHER terminates nor repeats.
Irrational numbers DO NOT consist of natural numbers, whole numbers, and integers. Basically,
whatever is not a rational number is an irrational number.
Examples:
  3.1416...
2  1.4142...

Real numbers: x x corresponds to a point on the number line
Real numbers
consist of all: Natural numbers, Whole numbers, Integers, Rational numbers, and Irrational
0
numbers
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 2
Example1:
2


List the elements of the set 4, 0, 7, 49, ,  134  that are also elements of the given set.
5


Whole numbers 0, 4, : 49
numbers:
Integers:
0, 4, 49,  134
2
Rational numbers: 0, 4, 49, ,  134 Irrational numbers: 7
5
Natural
4, 49
2
Real numbers: 0, 4, 49, 7, ,  134
5
Problems
Problems 1 - 4, determine whether each statement is true or false.
1. 4 is a real number.
2. Every rational number is an integer.
7
3.
is an irrational number.
8
4. -6 is an integer.
3


5. List the elements of the set 6,.1, 3, 36, ,  134  that are also elements of the given set.
8


Whole numbers:
Integer:
Natural
numbers:
Rational numbers:
Irrational numbers:
Real numbers:
9 
 3
6. List the elements of the set 3, , 5, 64, ,   that are also elements of the given set.
11 
 4
Whole numbers:
Integer:
Natural
numbers:
Rational numbers:
Irrational numbers:
Real numbers:
7 2 
1
7. List the elements of the set  ,  35, 9,  , , 2  that are also elements of the given set.
8 5 
5
Whole numbers:
Integer:
Natural
numbers:
Rational numbers:
Irrational numbers:
Real numbers:
[M80A/80 SUPPLEMENT: UNIT 1.2]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 3
3 4 

8. List the elements of the set 2, 6,.6, , , 7  that are also elements of the given set.
7 5 

Whole numbers:
Integer:
Natural
numbers:
Rational numbers:
Irrational numbers:
Real numbers:
6


9. List the elements of the set .25, , 81, 144,  45, 25 that are also elements of the given
10


set.
Whole numbers:
Integer:
Natural
numbers:
Rational numbers:
Irrational numbers:
Real numbers:


81
6
8

10. List the elements of the set  , 66,
, 17, ,  59, 0  that are also elements of the given
9
8
2



set.
Whole numbers:
Integer:
Natural
numbers:
Rational numbers:
Irrational numbers:
Real number:
[M80A/80 SUPPLEMENT: UNIT 1.2]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 4
Answers
1. True
2. False
3.
False
4.
True
Whole #s: 6, 36 ; Integers: 6,  134, 36 ; Natural #s: 6, 36 ; Rational #s:
3
6,.1,  134, 36,
8
3
Irrational #s: 3 ; Real #s: 6,.1, 3, 36, ,  134
8
5.
6.
Whole #s:
64 ; Integers: 3, 64 ; Natural #s:
3
9
64 ; Rational #s: 3, , 64,
4
11
3
9
Irrational #s:  , 5 ; Real #s: 3, , 5, 64, , 
4
11
Whole #s: 2, 9 ; Integers: 35, 2, 9 ; Natural #s: 2, 9 ; Rational #s:
7 2 1
35, 2, 9, , ,
8 5 5
7 2 1
Irrational #s: None ; Real #s: 35, 2, 9, , ,
8 5 5
7.
8.
Whole #s: 7 ; Integers: 2, 7 ; Natural #s: 7 ; Rational #s: 7,  2,.6,
Irrational #s:
4
5
3
3 4
6, ; Real #s: 2, 6,.6, , , 7
7
7 5
9. Whole #s: 25, 81, 144 ; Integers: 45, 81, 144, 25 ; Natural #s: 81, 144, 25 ;
6
Rational #s: .25, , 81, 144,  45, 25 ; Irrational #s: None ; Real #s:
10
6
.25, , 81, 144,  45, 25
10
10. Whole #s: 0,
81 8
81 8
, , 66 ; Integers: 59, 0,
, , 66 ; Natural #s:
9 2
9 2
Rational #s: 59, 0,
59, 0,
81 8
, , 66
9 2
81 8
6
, , 66, ; Irrational #s: 17 ; Real #s:
9 2
8
81 8
6
, , 66, 17, 0,
9 2
8
[M80A/80 SUPPLEMENT: UNIT 1.2]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.