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```2.1 The Real Numbers and Absolute Value
Objectives
• Compare real numbers.
• Simplify expressions involving opposites and
absolute value.
2.1 The Real Numbers and Absolute Value
Glossary Terms
absolute value
integers
irrational numbers
natural numbers
negative numbers
opposites
positive numbers
rational numbers
real numbers
whole numbers
2.1 The Real Numbers and Absolute Value
Rules and Properties
Sets of Numbers
Natural or counting numbers: N = 1, 2, 3, 4, . . .
Whole numbers: W = 0, 1, 2, 3, 4, . . .
Integers: I = . . . –3, –2, –1, 0, 1, 2, 3, . . .
2.1 The Real Numbers and Absolute Value
Rules and Properties
Definition of Rational Number: Any number
a
that can be expressed in the form , where a
b
and b are integers and b  0, is a rational
number.
Definition of Absolute Value: The absolute
value of a real number x is the distance from
x to 0 on a number line. The symbol |x| means
the absolute value of x.
2.1 The Real Numbers and Absolute Value
Key Skills
Compare values of real numbers.
Insert an ordering symbol to make each
statement true.
–12
a.
5
a.
5 is to the right of –12 on a number line, so
5 > –12.
9 is to the left of 17 on a number line, so
9 < 17.
b.
b.
9
17