**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**

**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.**

In other words, you will put your decimal after
the first non
zero number.

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.

** Example
1: **Write the number in scientific
notation:
734,000,000,000.

***Move decimal to create a
number between 1
and 10**

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.**

** Example
2: **Write the number in scientific
notation:
.000015.

***Move decimal to create a
number between 1
and 10**

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.**

**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 **

** Example
3: **Write the number in decimal notation without
exponents: .

** Example
4: **Write the number in decimal notation without
exponents: .

** Example
5: **Perform the indicated operation. Express the
answer in decimal form.

***Move the decimal 2 to the left**

** Example
6: **Perform the indicated operation. Express the
answer in decimal form.

***When
div. like bases you subtract your exponents: 30 - 25 = 5**

***Move the decimal 5 to the right**

** 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 bottom of this web page goes over scientific notation.

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

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.