Scientific Notation

Date: 04/03/99 at 23:11:26
From: Sanquetta Hallbrooks
Subject: Scientific Notation

Dear Dr. Math,

In school we are learning about scientific notation. While they were 
learning about and how to solve scientific notation, I was out sick 
for 3 weeks. How do I solve a problem like:

125678.098

I thought that you would solve the problem by bringing the decimal 
between the 1 and the 2. But I found out that there are other ways 
to solve the problem. My question is, are there really other ways? 
After you put the decimal between the one and the two, don't you write 
the other numbers after the one and the two times 10^5? Why does there 
always have to be 10 to the whatever power it will be? 

Thank you very much.

Sincerely yours,
Sanquetta

Date: 04/04/99 at 21:26:27
From: Doctor Rick
Subject: Re: Scientific Notation

Hi, Sanquetta, I'm glad you're better and I hope you can quickly get 
back on your feet academically! 

You have it right. A number written in scientific notation is always a 
number between 1 and 10, times 10 to a power. If you put the decimal 
point anywhere other than between the 1 and the 2, you would have a 
number that is either less than 1 (like 0.125678) or greater than 10 
(like 12.5678). There is no other choice.

Every time you move the decimal point one place to the left, it is the 
same as dividing the number by 10. To keep the number the same, you 
must multiply it by 10 at the same time:

  125678.098
  12567.8098 * 10
  1256.78098 * 10^2
  125.678098 * 10^3
  12.5678098 * 10^4
  1.25678098 * 10^5

All these represent the same number, but only the last is in correct 
scientific notation.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/