Scientific Notation: Exponents

Date: 8/29/96 at 16:8:24
From: PATRICIA A RAMEY
Subject: Name of Number...

The question has come up as to what to call anumber that has a 
decimal followed by 23 zeros and then the digit 2:

0.000000000000000000000002

Thank you,
Pat

Date: 8/29/96 at 22:3:27
From: Doctor Jodi
Subject: Re: Name of Number...

Hi Pat! Great question.  Have you ever heard of scientific notation?  
That's a system of writing numbers which is particularly useful for 
referring to very large and very small numbers.

Scientific notation uses the idea of exponents.  What's an exponent?  
Well, if I want to write

2 x 2 x 2 x 2 x 2

in shorthand, I could call it 2^5 (read 2 to the fifth power).  The 
five stands for the number of 2's.  Does that make sense?

Scientific notation is based on exponents with base 10.  (That means 
that 10 is the number you're multiplying.) For example, if I want to 
write 100, I first look at it as 10 x 10, then call it 10^2.  

Here are a couple of questions for you:


What does 10^3 mean?  How many zeros does it have?

How would you write 10,000 as an exponent?

Now suppose instead of 100, you want to write 254 using exponents.  
This is written 2.54 x 10^2.  Does that make sense?  Expressing 254 as 
2.54 x 10^2 is its SCIENTIFIC NOTATION.

Suppose I wanted to write .0254 instead.  Is there a way to do that?  
Sure! We just have to get a little more creative....

If I wanted to write .01, also called 1/100, as 10's multiplied by
each other, I could do it like this:

1/100 = 1/10 x 1/10

So really, instead of multiplying, I'm *dividing* by the 10's.  So 
instead of using POSITIVE exponents, we use NEGATIVE exponents.  So 
.01 is written as 10^(-2) or 1 X 10^(-2).

So your number could be written as

2 X 10^(-24)

in scientific notation.

I hope this helps; let us know if you have more questions...

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