College Algebra
Tutorial 3: Scientific Notation

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WTAMU > Virtual Math Lab > College Algebra
Learning Objectives
After completing this tutorial, you should be able to:
 Write a number in scientific notation.
 Write a number in decimal notation without exponents.

Introduction
This tutorial takes a look at the basic definition of
scientific notation,
an application that involves writing the number using an exponent on
10.
Since part of a number that is written in scientific notation is 10
raised
to a power, when we multiply or divide these types of numbers we need
to
remember some of our exponent rules. If you need to review your
exponent
rules, feel free to go to Tutorial
2:
Integer Exponents. Like it or not, the best way to
master
these problems is to work through them. So I guess we better
get to it. 
Tutorial
Scientific Notation
A positive number is written in
scientific notation
if it is written in the form:
where 1 < a <
10 and r is
an integer power of 10.

Writing a Number in Scientific
Notation

Step 1:
Move the
decimal point so that you have a number that is between 1 and 10. 
In other words, you will put your decimal after
the first non
zero number. 
Step 2:
Count
the number of decimal places moved in Step 1 . 
If the decimal point was moved to the left, the count
is positive.
If the decimal point is moved to the right, the count is
negative. 
Step 3:
Write
as a product of the number (found in Step 1) and 10 raised to the power
of the count (found in Step 2). 

*Decimal is at the end of the
number
*Move decimal to create a
number between 1
and 10 
How many decimal places did we end up moving?
We started at the end of the number 734,000,000,000 and moved it
between
the 7 and 3. That looks like a move of 11 places.
What direction did it move?
Looks like we moved it to the left.
So, our count is +11. 
Note how the number we started with is a bigger
number than the
one we are multiplying by in the scientific notation. When that
is
the case, we will end up with a positive exponent. 

*Decimal is at the beginning
of the number
*Move decimal to create a
number between 1
and 10 
How many decimal places did we end up moving?
We started at the beginning of the number .000015 and moved it
between the 1 and 5. That looks like a move of 5 places.
What direction did it move?
Looks like we moved it to the right.
So, our count is  5. 
Note how the number we started with is a smaller
number than the
one we are multiplying by in the scientific notation. When that
is
the case we will end up with a negative exponent. 
Write a Scientific Number in
Standard Form

Basically, you just multiply
the first number
times the power of 10.
Whenever you multiply by a power of 10, in
essence what you are
doing is moving your decimal place.
If the power on 10 is positive, you move the
decimal place that many
units to the right.
If the power on 10 is negative, you move the
decimal place that many
units to the left.
Make sure you add in any zeros that are
needed 


*Move the decimal 7 to the right


*Move the decimal 4 to the left


*Move the decimal 2 to the left 
Practice Problems
These are practice problems to help bring you to the
next level.
It will allow you to check and see if you have an understanding of
these
types of problems. Math works just like
anything
else, if you want to get good at it, then you need to practice
it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.
In fact there is no such thing as too much practice.
To get the most out of these, you should work the
problem out on
your own and then check your answer by clicking on the link for the
answer/discussion
for that problem. At the link you will find the answer
as well as any steps that went into finding that answer.

Practice
Problem 1a: Write the number in scientific
notation.
Practice
Problem 2a: Write the number in decimal
notation, without
exponents.
Practice
Problems 3a  3b: Perform the indicated
operation. Express the answer in decimal form.
Need Extra Help on these Topics?
The following are webpages
that can assist
you in the topics that were covered on this page:

WTAMU > Virtual Math Lab > College Algebra
Videos at this site were created and produced by Kim Seward and Virginia Williams Trice.
Last revised on Dec. 4, 2009 by Kim Seward.
All contents copyright (C) 2002  2010, WTAMU and Kim Seward. All rights reserved.
