Decoding Place Value

Date: 09/14/2003 at 18:02:20
From: Samantha
Subject: base 10

What does it mean to be in base 10?  What does the 1 represent?  What 
does the 0 represent?

I think I understand the 1 to represent one 10, but I'm a little 
confused about the 0.  Does it mean that there are no units left over 
from base 10?

Date: 09/15/2003 at 13:41:48
From: Doctor Ian
Subject: Re: base 10

Hi Samantha, 

When we write a number like 

  2034

each digit is multiplied by some power of 10, and the results are
added up.  That is, 
                   
      2034 = 2*1000   + 0*100    + 3*10     + 4*1
 
              ^          ^          ^          ^
              |          |          |          |
            2 groups  0 groups    3 groups   4 groups
            of 1000   of 100      of 10      of 1
              |          |          |          |
              |          |          |          |
     2000  <--           |          |          |
      000  <-------------           |          |
       30  <------------------------           |
   +    4  <-----------------------------------
   ------
     2034 

Does this help? 

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

Date: 09/15/2003 at 19:08:29
From: Samantha
Subject: Thank you (base 10)

Thank you for your help! It made it much easier to 
understand.  The example was great!  Thanks again.