Download 8.1 Symbols and Sets of Numbers

8.1
Symbols and Sets of Numbers
Learning Objectives:
1. Define the meaning of the symbols: =, ? , <, >, ≤ , and > .
2. Translate sentences into mathematical statements.
3. Identify integers, rational numbers, irrational numbers, and real numbers.
4. Find the absolute value of a real number.
5. Key Vocabulary: set, member, element, number line, integers, rational numbers, irrational
numbers, real numbers, absolute value.
Definitions:
1. Natural Numbers-are counting numbers.
2. Whole Numbers-are counting numbers and 0.
A. Equality and Inequality Symbols
Equality symbol
Inequality symbols
Order Property for Real Numbers: For any two real numbers a and b,
1. a is less than b if a is to the left of b on the number line.
2. a is greater than b if a is to the right of b on the number line.
Example 1. Insert <, >, or = in the space between the paired numbers to make each statement true.
a.
2.12 _________ − 2.12
b.
3
9
______________
7
21
Example 2. Determine whether each statement is true or false.
14 7
a. 15 < 20
b. 3.002 > 3.202
c.
≠
18 9
B. Translating sentences into mathematical statements
Example 3. Translate each sentence into a mathematical statement.
a.
Negative eleven is less than or equal to negative four.
b.
Fourteen is greater than one.
d.
6 11
≥
7 14
C.
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
-6 -5 -4 -3 -2 -1
1
0
2
3
4
5
6
7
8
Definitions:
1. Integers-are positive, negative numbers and zero.
3.
a
Rational Numbers- are any numbers that can be written as  a and b are interger and b ≠ 0 .
b

Irrational Numbers-are nonrational numbers that correspond to points on the number line.
4.
Real Numbers-are all numbers that correspond to points on the number line.
5.
Absolute Value, a -is the distance between a and 0 on the number line.
2.
Real numbers
Irrational numbers
rational numbers
Noninteger Rational
integers
negative integers
whole number or
positive integers
zero
Natural number or
positive integers
Example 4. Tell which set or sets each number belongs to: natural numbers, whole numbers,
integers, rational numbers, irrational numbers, and real numbers.
Real number
Natural
number
Whole
number
Rational
number
Irrational
number
5
8
3
5
−2
0
Example 5. Find each absolute value.
a.
6.2
b. − 14
Example 6.
0
Place the following numbers on the number line provided:
13
,
4
-6
c.
-5
-4
−
-3
1
,
3
-2
−
-1
7
,
2
0
7
10
1
2
3
4
5
6
7
8
Integer
number