28 CHAPTER 1 The Real Number System
OBJECTIVES
Real Numbers and the Number Line
1.4
1 Classify numbers
and graph them on
number lines.
2 Tell which of two
real numbers is less
than the other.
3 Find the additive
inverse of a real
number.
4 Find the absolute
value of a real
number.
5 Interpret the
meanings of real
numbers from a
table of data.OBJECTIVE 1 Classify numbers and graph them on number lines.In
Section 1.1,we introduced the set of natural numbersand the set of whole numbers.
Natural Numbers5 1, 2, 3, 4,Á 6 is the set of natural numbers(or counting numbers).
Whole Numbers5 0, 1, 2, 3, 4,Á 6 is the set of whole numbers.
NOTE The three dots show that the list of numbers continues in the same way
indefinitely.
1 Á 2
0123456These points correspond to natural numbers.These points correspond to whole numbers.
FIGURE 3To draw a number line, choose
any point on the line and label it- Then choose any point to the
right of 0 and label it 1. Use the
distance between 0 and 1 as the
scale to locate, and then label,
other points.
The natural numbers are located to the right of 0 on the number line. For each nat-
ural number, we can place a corresponding number to the left of 0, labeling the
points and so on, as shown in FIGURE 4. Each is the opposite,or
negative,of a natural number. The natural numbers, their opposites, and 0 form the
set of integers.
- 1, -2, -3,
Negative numbers Positive numbers–3–2–10123Zero
(neither positive nor negative)Opposites
The points correspond to integers.
FIGURE 4Integers5 Á, -3, -2, -1, 0, 1, 2, 3,Á 6 is the set of integers.
We can represent numbers on a number linelike the one in FIGURE 3.
Positive numbersand negative numbersare called signed numbers.
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