Home
#### Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test
#### Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator
#### Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets

Home » Exponents »
Scientific Notation

# Scientific Notation

## Shortcut:

## Example 1

## Example 2

## Example 3

## Example 4

## TIP:

## Example 5

## Example 6

## Example 7

## You Might Also Like These Exponent Lessons:

# Like This Page?

Since we've done so much work with exponents, we are going to continue our studies by looking at scientific notation.

Scientific notation is simply a "shorter way" of writing very large or very small numbers.

Scientists often work with very large or extremely small numbers when performing experiments, which is why it is called "scientific" notation.

There is a specific format in which you must write a number in order for it to be considered scientific notation. Let's take a look:

It's really important that you understand the format for scientific notation, so let's look at a chart that illustrates a few incorrect and correct ways to write numerals in scientific notation.

Are you wondering why we have to multiply by 10 to a power? Why 10 and not 5 or 3? Take a look at this quick example.

Do you see the pattern? We continue to add a 0, or another place to the number three.

Notice that the three itself remains unchanged. We just continue to add a 0, when we multiply by a larger power of 10.

When you multiply by a positive power of 10, you can simply move the decimal point to the right the same amount of spaces as the exponent.

Let's take a look at a couple of examples of numbers written in scientific notation and rewrite them in expanded form.

Now, let's look at a few examples in expanded form and rewrite them in scientific notation.

So, how are you feeling about scientific notation when the power of 10 is positive? It gets easier as you practice a little more, I promise! Are you ready to look at a few problems where the power of 10 is negative? Don't worry - same process, we're just going to move the decimal in a different direction!

If you studied the lesson on negative exponents, then you learned that when you raise a whole number to a negative power, it results in a fraction because you take the recipocal.

And... we all know that proper fractions have a smaller value than whole numbers. So, when we work with powers of 10 to a negative power, we are going to be working with very small numbers.

If you have a negative power of 10, you must move the decimal point to the left! We are creating a smaller number!

Let's take a look at a couple of examples written in scientific notation and expand them.

Let's look at one more example. I've given you the expanded form this time, and would like to show you how to write it in scientific notation. Pay special attention to where I stop counting when I move my decimal to the right.

Awesome Job! In the next lesson, we'll take a look at more difficult problems involving scientific notation! See you there!

**Exponents Unit:**

Sign Up for Algebra Class E-courses

Click here to retrieve a lost password.

Custom Search

Most Popular Pages

*"I'd like to start off by relaying my sincerest gratitude for your dedication in teaching algebra. Your methodology is by far the simplest to follow, primarily because you take the time to include the small steps in between that most other teachers leave out.*

*It helps to know why you are doing something. I am 45 and heading to college to get my BS in Business. I need to brush up, hence the visit to your site. Great Job!"*

Jimmy - United States

*"I stumbled onto your site after I found out that I needed to use some fundamental algebra for an assignment. Turns out I had forgotten some things and your great site helped me remember them like "that" (snap of fingers). The organization of the site let me find exactly what I was looking for so easily. Kudos to you for maintaining such a great resource for students of all ages!"*

Tom - United States

*"I just wanted to write and basically thank you for making such a wonderful website! I'm 20 years old and about to take a basic placement test for college. I wanted to brush up on my Algebra skills and I stumbled upon your site. I'm amazed at how simple you make it and how fast I'm remembering Algebra! I don't remember getting most of the answers right when I had an actual teacher in front of me teaching this. Thanks a lot!"*

Elizabeth - United States

*"I am a pensioner living in South Africa. I stumbled on your website, the best thing that could ever happen to me! Your course in Algebra has helped me a lot to better understand the different concepts. Thank you very much for sharing your skills for teaching math to even people like me. Please do not stop, as I am sure that your teachings have helped thousands of people like me all over the world."*

Noel - South Africa

*This is an amazing program. In one weekend I used it to teach my Grade 9 daughter most of the introductory topics in Linear Relations. I took her up to Rate of Change and now she can do her homework by herself.*

Reg - United States

- Algebra Class E-course
- Algebra Class Products
- Print this Site
- Algebra Practice Test
- Algebra Readiness Test
- Homework Answer Calculator
- Practice Worksheets

- Site Map
- Pre-algebra Refresher
- Solving Equations
- Graphing Equations
- Writing Equations
- Systems of Equations
- Inequalities
- Functions
- Exponents & Monomials
- Polynomials
- Quadratic Equations
- Algebra 1 Final Exam

? ## Subscribe To This Site

Then why not use the button below, to add us to your favorite bookmarking service?

Copyright © 2009-2014 Karin Hutchinson ALL RIGHTS RESERVED

## Comments

We would love to hear what you have to say about this page!