MAT013
Applied Math I
Procedures
Scientific Notation Steps
The process for using numbers expressed in Scientific Notation is somewhat complicated, but
can be easily accomplished one step at a time, while carefully using what we have learned about
operations with signed numbers, operations with Powers of 10, and expressing numbers in
Scientific Notation.
The steps are:
1. Express all numbers in Scientific Notation.
2. Create 2 problems
a. Arithmetic
b. Powers of 10
3. Perform all Arithmetic operations
4. Perform all Powers of 10 operations using signed numbers correctly.
5. Combine the two parts
6. Express in proper Scientific Notation.
a. Express Arithmetic part in Scientific Notation.
b. Perform the Powers of 10 operations using signed numbers
correctly.
c. The final answer should be in proper Scientific Notation.
Remember:
Proper Scientific Notation has only and exactly one digit to the left of the
decimal point. The Power of 10 represents the number of places the
decimal point has been moved. The sign of the Power of 10 is determined
by the direction the decimal point has been moved.
I have demonstrated an Example, Step by Step on the next page.
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MAT013
Applied Math I
Procedures
Scientific Notation Steps
Continued
Example:
Steps: 1.
2.
 18.6  2100 


 0.036  950 
8
Express all numbers in Scientific Notation




 1.86  101 2.1  10 3

2
2
 3.6  10 9.5  10
Create 2 problems
a.
Arithmetic
b.
 (1.86)( 2.1) 


 (3.6)(9.5) 
Powers of 10
 
 
8
8
8
3.
 101  10 3 
  2

2 
 10  10 
Perform all Arithmetic operations 4.
 3.906 


 34.2 
10 
0.11428
5.
6.
Note:
Perform all Powers of 10 operations
 10 4
 0
 10
8



8
4 8
0.000000029
Combine the two parts
0.000000029 X 1032
1032
Express in proper Scientific Notation.
a.
Express Arithmetic part in Scientific Notation.
2.9 X 10-8
b.
Perform the Powers of 10 operations
10-8 X 1032 = 1024
c.
The final answer should be in proper Scientific Notation.
2.9 X 1024
Performing each step carefully, using all the tools we have learned, will lead to the
correct answer.
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