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### 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

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)

understand.  The example was great!  Thanks again.
```
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