Dividing by Powers of 10

Date: 09/12/98 at 15:26:50
From: Grace
Subject: Dividing by 100, 1000...

Dear Dr. Math,

My sister (6th grade) can't figure out how to divide by numbers like 
100, 1000 and so on. My mom and I just can't figure out how to explain 
it to her. Please tell me how to explain it to her so that she can 
understand.

Grace
Paris, France

Date: 09/14/98 at 09:16:42
From: Doctor Peterson
Subject: Re: Dividing by 100, 1000...

Hello, Grace. 

If what I have to say doesn't help, you may need to tell me how you 
have tried to explain it and what objections she gives, and perhaps 
also what else she does understand so we can find the best way to 
relate this new idea to what she knows. Or perhaps she understands it 
in simple cases but has trouble if there is no decimal point or if 
extra zeroes have to be added.

Assuming your sister is working with decimals, it's very simple: to 
divide by 10, move the decimal point one place to the left; to divide 
by a power of 10, move it one place to the left for each zero in the 
number. For example:

    123 / 10 = 12.3       123.
           -                / left one place
           one zero       12.3

    123 / 100 = 1.23      123.
           --               / left two places
           two zeroes      /
                          1.23

If she doesn't believe this, she can just do the long division and see 
how the answer comes out. You could also explain it in terms of place 
value. If you divide by ten, hundreds become tens, tens become ones, 
and ones become tenths:

    123 = 1 hundred, 2 tens, 3 ones
              |         |       |
              |         |       |  divide by ten
              v         v       v
          1  ten,    2 ones, 3 tenths = 12.3

Each zero in 100 means one more ten to divide by, so there is one more 
decimal place to move.

Let me know if that helps!

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/