Download Properties of Real Numbers

Properties of Real Numbers
Objective:
(1) To graph and order real numbers
(2) To identify and use properties of real
numbers
Subsets of Real Numbers
Rational Numbers
3
,8,0.14,0. 3
5
Integers
... -3, -2, -1, 0, 1, 2, 3…
Whole Numbers
0, 1, 2, 3, …
Natural/Counting Numbers
1, 2, 3, …
Irrational Numbers
2, , e
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.
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
Example #2: Graphing Numbers on a
Number Line
Graph the numbers
-3/2, 1.7, 5

-4
-2
 
0
2
4
Example #3: Finding Inverses
Find the opposite and the reciprocal of each
number.
3
a. -3.2
b. 5
3

3.2
opposite
5
3 .2
reciprocal 5
3 .2 
1
3 .2
1

1
3. 2
1
10
5


3.2 32 16
3
Example #4: Finding Absolute Value
Find each absolute value:
a. 12
 12
b. -5.6
 5.6
c. 5 – 8
 -3

3