Why Multiplying by 10 Just Adds a Zero at the End

Date: 10/18/2005 at 11:08:41
From: Jill
Subject: Explanation of multiplying by 10

My daughter is learning multiplication and is having a hard time 
figuring out why if you add a zero to a number while multiplying by 10
it works.  Her teacher is unable to get through to her and I was 
looking for a way to explain this better.  Something concerning place
value but don't know how to explain to a 8 year old!

Date: 10/18/2005 at 16:58:10
From: Doctor Peterson
Subject: Re: Explanation of multiplying by 10

Hi, Jill.

We may have to make a few attempts before we meet her particular style 
of learning, but here's my first method.

Look at a number like 123. This means

  100 + 20 + 3

because the 1 is in the hundreds column, the 2 is in the tens, and 
so on.

Now put a 0 at the end, to make 1230.  Suddenly the 1 has moved into 
the thousands column, the 2 is in the hundreds column, and so on. 
Every digit has been shoved over, so that it is worth 10 times what it
was worth before.  It's as if I took your wallet and replaced every 
one dollar bill with a ten, every ten with a hundred, and so on.  The 
total is worth ten times what it was.

That's what's happening here.

If that doesn't work, please write back.


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