Beginning Algebra, 11th Edition

SECTION 1.4 Real Numbers and the Number Line^29

Equivalent Quotient

Rational Number of Two Integers

0.23

(terminating decimal)

or

(repeating decimal)

4.7^4710 1 means 47, 102

1

3 1 means 1,^32

0.3333Á, 0.3

23

100 1 means 23,^1002

7

1 4 1 means 7, 42

3

4

• 5


• 5 1 1 means - 5 , 12

Using Negative Numbers in Applications

Use an integer to express the number in boldface italics in each application.

(a)The lowest Fahrenheit temperature ever recorded was 129 ° below zero at Vostok,

Antarctica, on July 21, 1983. (Source: World Almanac and Book of Facts.)

Use 129 because “below zero” indicates a negative number.

(b)General Motors had a loss of about $ 31 billion in 2008. (Source: The Wall Street

Journal.)

Here, a loss indicates a negative “profit,” NOW TRY

Fractions, introduced in Section 1.1,are examples of rational numbers.

- 31.

-

NOW TRY EXAMPLE 1

EXERCISE 1
Use an integer to express the
number in boldface italics in
the following statement.

At its deepest point, the floor
of West Okoboji Lake sits
136 ft below the water’s
surface. (Source:
http://www.watersafetycouncil.org))

NOW TRY ANSWER

1. 
   
   
   
   • 136
   
   
   
   

Rational Numbers

is a quotient of two integers, with denominator not 0 is the set of rational

numbers.

(Read the part in the braces as “the set of all numbers xsuch that xis a quo-

tient of two integers, with denominator not 0.”)

5 x|x 6

NOTE The set symbolism used in the definition of rational numbers,

is called set-builder notation.We use this notation when it is not possible to list all

the elements of a set.

{x|x has a certain property},

Since any number that can be written as the quotient of two integers (that is, as a

fraction) is a rational number, all integers, mixed numbers, terminating (or ending)

decimals, and repeating decimals are rational.The table gives examples.

To grapha number, we place a dot on the number line at the point that corresponds

to the number. The number is called the coordinateof the point. See FIGURE 5.

–2 –1 012 3 4

3

• 2
  2


• 3
  1
  2

4

1

23

8

1

(^13)
1
(^34)
Graph of selected rational numbers
Graph of
4
Coordinate
FIGURE 5
Think of the graph of
a set of numbers as a
picture of the set.
Think: - 32 =- 1 12 Think:^238 = (^2 78)