Basic Mathematics for College Students

132 Chapter 2 The Integers

SECTION 2.1

An Introduction to the Integers

We have seen that whole numbers can be used to describe many situations that arise

in everyday life. However, we cannot use whole numbers to express temperatures

below zero, the balance in a checking account that is overdrawn, or how far an object

is below sea level. In this section, we will see how negative numbers can be used to

describe these three situations as well as many others.

RECORD ALL CHARGES OR CREDITS THAT AFFECT YOUR ACCOUNT

NUMBERDATE DESCRIPTION OF TRANSACTION PAYMEN(– )T/DEBIT

$$$

√T(IF F(A+EEN)Y)DEPOSIT(+/C)REDIT$ BALANCE

1207 Wood's Auto RepairTransmission 500 00

450 00

5

2

The record cold temperature in

the state of Florida was 2 degrees

below zero on February 13, 1899,

in Tallahassee.

A check for $500 was written

when there was only $450 in the

account. The checking account

is overdrawn.

The American lobster is found off

the East Coast of North America at

depths as much as 600 feet below

sea level.

Tallahassee

1 Define the set of integers.

To describe a temperature of 2 degrees above zero, a balance of $50, or 600 feet above

sea level, we can use numbers called positive numbers.All positive numbers are

greater than 0, and we can write them with or without a positive sign.

In words In symbols Read as

2 degrees above zero or 2 positive two

A balance of $50 or 50 positive fifty

600 feet above sea level or 600 positive six hundred

To describe a temperature of 2 degrees below zero, $50 overdrawn, or 600 feet

below sea level, we need to use negative numbers.Negative numbersare numbers less

than 0, and they are written using a negative sign.

In words In symbols Read as

2 degrees below zero negative two

$50 overdrawn negative fifty

600 feet below sea level negative six hundred

Together, positive and negative numbers are called signed numbers.

 600

 50

 2



 600

 50

 2



Objectives

1 Define the set of integers.

2 Graph integers on a number line.

3 Use inequality symbols to

compare integers.

4 Find the absolute value of an

integer.

5 Find the opposite of an integer.