Page 140 - Basic College Mathematics with Early Integers

S E C T I O N 2.2 I INTRODUCTION TO INTEGERS 117

Example 1 Representing Depth with an Integer PRACTICE 1
a. The world’s deepest bat
The world’s deepest cave is Krubera (or Voronja), in the country of Georgia, colony spends each winter in
located by the Black Sea in Asia. It has been explored to a depth of 6824 feet a New York zinc mine at a
below the surface of the Earth. Represent this position using an integer. depth of 3805 feet. Represent
(Source: Guinness World Records) this position with an integer.
Solution: If 0 represents the surface of the Earth, then 6824 feet below the (Source: Guinness Book of
surface can be represented by -6824. World Records)
b. The tamarack tree, a kind of
Work Practice 1
larch, commonly grows at the
edge of the arctic tundra and
Objective Graphing Integers survives winter temperatures
of 85 degrees below zero,
Fahrenheit. Represent this
Example 2 Graph 0, -3, 2, and -2 on the number line. temperature with an integer
in degrees Fahrenheit.
Solution:
5 4 3 2 1 0 1 2 3 4 5
Work Practice 2

Objective Comparing Integers
We can compare integers by using a number line. For any two numbers graphed on a
number line, the number to the right is the greater number and the number to the
left is the smaller number. Also, the symbols 6 and 7 are called inequality symbols.
The inequality symbol> means “is greater than” and
the inequality symbol< means “is less than.”

For example, both -5 and -7 are graphed on the number line below. PRACTICE 2
Graph -5, -4, 3, and -3 on
8 7 6 5 4 3 2 1 0 1 2 the number line.
On the graph, -7 is to the left of -5 , so -7 is less than -5 , written as 5 4 3 2 1 0 1 2 3 4 5

-7 6-5
We can also write
-5 7-7

since -5 is to the right of -7, so -5 is greater than -7.
PRACTICE 3
Concept Check Is there a largest positive number? Is there a smallest nega- Insert 6 or 7 between each
tive number? Explain. pair of numbers to make a true
statement.
a. 0 -3
Example 3 Insert 6 or 7 between each pair of numbers to make a true b. -5 5
statement.
c. -8 -12
a. -7 7 b. 0 -4 c. -9 -11
Answers
Solution: 1. a. -3805 b. -85°F
2.
a. -7 is to the left of 7 on a number line, so -7 6 7. 5 4 3 2 1 0 1 2 3 4 5
b. 0 is to the right of -4 on a number line, so 0 7-4. 3. a. 7 b. 6 c. 7
c. -9 is to the right of -11 on a number line, so -9 7-11.
Concept Check Answer
Work Practice 3 No