Multiplying by Zero

Date: 10/19/2002 at 14:47:10
From: Carley
Subject: Project on zero

Dear Dr. Math, 

I know that zero's value is nothing, but why is it that it turns other 
numbers that clearly have a greater value to zero when multiplied? I 
have tried to answer that question in my research so far but I have 
been unsuccessful.

Thank you so much.
Sincerely, 
Carley

Date: 10/19/2002 at 18:02:52
From: Doctor Ian
Subject: Re: Project on zero

Hi Carley,

If I understand your question correctly, you want to know why, if you 
multiply zero by _anything_, no matter how big, you get zero as a 
product:
 
                              1 * 0 = 0

                             27 * 0 = 0
 
  1,887,457,234,543,243,113,946 * 0 = 0

When you multiply one number by another, you can think of starting at 
some point ('the spot marked X', or wherever) and moving some distance 
away from it. To move, you need to know two things:

  1) how many steps you're going to take

  2) how big each step will be

Now, if each step is of zero size, then you can keep taking them, and 
you'll never move anywhere. (Move a step of length zero. You're still 
where you started. Do it again. Still there. Keep doing it... how many 
of those steps will you have to take to actually move somewhere?) So 
any number times zero is still zero.

Also, if you're not going to take any steps, it doesn't matter how 
large a step you _would_ take, since you're not going to take it. So 
zero times any number is still zero. 

Does this make sense? 

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