1. Properties of Real Numbers
Objective:
To graph and order real numbers
To identify and use properties of real numbers

2. Subsets of Real Numbers
Rational Numbers
Irrational Numbers
Integers
... -3, -2, -1, 0, 1, 2, 3…
Whole Numbers
0, 1, 2, 3, …
Natural/Counting Numbers
1, 2, 3, …

3. Definitions
Opposite (additive inverse): The opposite of any number a is –a. The sum of opposites is 0. Reciprocal (multiplicative inverse): The reciprocal of any non-zero number a is 1/a. The product of reciprocals is 1. Absolute Value: The absolute value of a number is the number’s distance from zero on the number line.

4. Example #1: Determining Number Sets
Which set of numbers best describes the values for each variable?
The cost C of admission for p people.
C is rational, p is a whole number
A company’s profit (or loss) P in dollars for each quarter q.
P is rational, q is a whole number
The ratio of a circle’s circumference C with diameter d
C is irrational, d is rational

5. Example #2: Graphing Numbers on a Number Line
Graph the numbers /2, 1.7,    -4 -2 2 4

6. Example #3: Finding Inverses
Find the opposite and the reciprocal of each number. b.
opposite
reciprocal

7. Example #4: Finding Absolute Value
Find each absolute value:
12 12
-5.6
5.6
5 – 8
-3 3