Why the Decimal Point Moves when Multiplying by 10

Date: 02/11/2005 at 21:37:08
From: Stacie
Subject: decimal point movement

I am trying to explain why when you multiply a number by 10 you move 
the decimal point over one place to the right, and one place to the 
left when you divide by 10.  I know there are ten 10's in 100, and I'm 
sure that has something to do with it, but I just can't get the exact 
words in my head.  Could you maybe point me in the right direction?

Date: 02/11/2005 at 23:03:43
From: Doctor Peterson
Subject: Re: decimal point movement

Hi, Stacie.

Each "place" in a number is worth ten times as much as the place to
its right.  So when you multiply a number containing only one nonzero
digit by ten, you move that digit one place to its left:

  200 * 10 = 2000
  ^          ^
  |          |
  |          +--- thousands
  |
  +-------------- hundreds

Any number is the sum of numbers of this form:

  123 = 100 + 20 + 3

Multiply that by ten, and _each_ digit moves one place to the left:

  123 * 10 = 1000 + 200 + 30 = 1230

If we look at this from a different perspective, rather than the 
digits moving to the left, we can see the places (measured from the
decimal point) moving to the right, so that the place that was the 
tens place moves to where the ones place was:

    1 2 3     1 2 3.0
   / / /            \
  1 2 3 0     1 2 3 0.

So what was 1 hundred is now 1 thousand, and so on.

If you have any further questions, feel free to write back.


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