Math 114
Scientific Notation
Powers of Ten
Standard Scientific
Notation
n is an integer
Using Scientific
Notation
The population of
To change the number into scientific notation you move the
decimal place seven places to get: 
The speed the speed of light is 30,000,000,000 m/s. Write this number in scientific notation.
Answer: 
Convert .00000079 to scientific notation
Answer: 
Convert .000000000043
Answer: 
Multiplication with
scientific notation
Examples
1) Simplify
2) Simplify
3) Simplify
Division
Examples
4) Simplify
5) Simplify
6) Simplify
Sets and Set notation
Introduction to Sets
Common sets
The natural numbers
The whole numbers
The integers
Specifying a set by
roster form
Examples
1) Specify the set {The U. S. Presidents since 1980} by roster
Answer: {Ronald Reagan, George Bush Sr., Bill Clinton, George Bush Jr.}
2) Specify the set 
in builder set
notation by roster
Answer: 
Specifying sets by
builder set notation
1) Specify the following set in builder set notation.
2) Specifying the following set in builder set notation.
{1,3,5,7,……..}
Answer: {x | x is an odd integer}
3) Specify the following set in Builder set notation.
{Huron,
{x | x is a great lake}
Page 118
Write each set in roster form
18) {Positive multiples of 3}
Answer in roster form: {3,6,9,12,15,18,21,……}
20) {Counting numbers greater than 150}
Write each set in builder set notation.
24)
{1,11,121,1331,14641,……}
{x | x is a power of 11}
Definitions
Infinite Set: A set that has an infinite number of elements.
Finite Set: A set that has a finite number of elements.
Examples
Finite Sets
Infinite Sets
{x | x is an odd integer}
Elements of a set
The statement 3 is an element of the set {1,2,3,4,5,6} in symbol form is written as follows: 
The statement 2 is not an element of (1,3,5,7} would be written as follows:
True or False
1)
2)
3)
The Empty Set
The empty set is a set that contains no elements. The empty set is also referred to as the null set.
Symbol representation 
or {}
Definition
Subset: A set B is a subset of a second set B if every element of the subset B is of the second set C.
Example 1
Let A={1,2,3,4,5},B={1,3,5,7},C={1,2,3},D={1,2,3,4,5}, and
E=
1) Is
Answer: Yes, every element in C is contained in
A
2) Is
Answer: No, the element 7 of set B is not contained in A.
3) Is
Answer: Yes, every element of D is in A.
4) Is
Yes, the empty set is a subset of nonempty
every set.
Note: The empty set is a set of every nonempty set. Every nonempty set is a subset of itself.
Example 2
List all subsets of the set {1,2}
Possible subsets
Example 3
List all subsets of the set {a,b,c}
Possible subsets
Example 4
List all subsets of the set {4}
Possible sets: 
The pattern for
subsets
|
Number of elements |
Number of subsets |
|
1 |
2 |
|
2 |
4 |
|
3 |
8 |
|
4 |
16 |
Formula to find the
number of subsets s of a given set A with n elements
Example 5
How many subsets does a set A with 6 elements have?
Equivalent Sets
Two sets are equivalent if they have the same number of elements.
Examples of equivalent sets
7) Simplify
