Scientific Notation

Date: 01/16/97 at 19:49:00
From: Fran Sherwood
Subject: Scientific notation

How do you write a number in scientific notation?

Date: 01/17/97 at 12:51:17
From: Doctor Wallace
Subject: Re: Scientific notation

Hi Fran!

Scientific notation is usually used to express numbers that are either 
very very large, or very very small. It's a way of writing these 
numbers so that they don't take up a lot of space.

A number written in scientific notation is made up of two parts, a 
decimal part, and a power of 10. For example, 2.1 x 10^6 is a number 
written in scientific notation. The 2.1 is the decimal part, and the 
10^6 is the power of ten (the ^ symbol here means that the 6 is the 
exponent).

Numbers in scientific notation are really multiplication expressions.  
We would read the above number as "2.1 times 10 to the sixth." Since 
10^6 is 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000, then 2.1 times this 
is 2,100,000.

Now for your question. How do we write a number in scientific 
notation?  It's easier than it looks. Say we have a number like 43.  
To write this or any other number in scientific notation, we have to 
"pull out" the power of ten inside the number.  

What power of 10 is in 43?  Well, it's 10^1 or 10. To keep the value 
of 43, when we pull out this 10^1, we need to decrease 43 by 1/10, 
or divide it by 10.  We get 43 divided by 10 = 4.3 when we do this.  
So 43 in scientific notation is 4.3 x 10^1.  Written another 
way, this is 4.3 x 10 = 43.    

Now, what if we had 430 to write in scientific notation?  Well, we'd 
pull out the next higher power of 10, 10^2 (which is 100), and divide 
430 by 100 and get 4.3 again.  So 430 = 4.3 x 10^2.

Have you spotted the easy way to figure out which power of ten to pull 
out yet?  If you haven't, think about it for a bit before reading 
further.

Here's how:  Take your number, and move the decimal point to the left 
until it stops between the first two digits in your number.  Count how 
many places you have to move it, and that's the power of 10 you need. 

Here's an example:

   1,244 is what in scientific notation?  

We move the decimal point to the left until it's between the first two 
digits, so we have 1.244. Then we count how many places it moved: 3.  
So,

   1,244 = 1.244 x 10^3  

Here's another example:

   1,544,433 = 1.544433 x 10^6

This method will only work for changing numbers that are greater 
than 1.  If you need to change a very small number like .032454 into 
scientific notation, then the procedure is just a little different.  
Maybe you can figure it out on your own.

Thanks for writing!

-Doctor Wallace,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/