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### 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/
```
Associated Topics:
Elementary Division
Elementary Place Value
Middle School Division

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