2.1: Use Integers and Rational Numbers
Whole Numbers: 0, 1, 2, 3, …
Integers: Whole positive numbers, whole negative numbers, and zero.
We can graph integers on a number line.
Example: Graph -4 and 6 on a number line.
Rational Numbers: are fractions, decimals that terminate (stop) or repeat, perfect
square roots, positive numbers, negative numbers, and zero.
We can use these definitions to classify numbers.
Example: Tell whether each of the following numbers is a whole number,
integer, or a rational number.
Number
Whole Number
Integer
Rational Number
5
Yes
Yes
Yes
0.6
No
No
Yes
2
3
No
No
Yes
-24
No
Yes
Yes
2

Opposites: 2 numbers that are the same distance from 0 on a number line but are
on opposite sides of 0.
Example: 2 and -2
Absolute Value: the distance between a number a and 0 on a number line.
2 2
0 0
Examples:
2  2
 2  2
 2  2

Conditional Statement: Has a hypothesis and a conclusion, and is normally written
in an if-then statement.
Example: If it is cloudy then it is raining.
In math, if a conditional statement is true, then the hypothesis and the conclusion in
the conditional statement is always true.
If the conditional statement is false, then the if-then statement is false for at least
one example. This example is called a counterexample.
Example of a conditional statement and a counterexample:
Conditional Statement: If a number is a rational number, then the number is
an integer.
The statement is false; a counterexample is the number 0.25. 0.25 is a
decimal, so it is a rational number but it is not a positive whole
number so it is not an integer.