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Multiplying by a Power of Ten

Date: 10/31/2001 at 11:08:19
From: Mike
Subject: Give the power of ten (decimals)

Dear Dr. Math,

Can you help me with this problem? The directions are:

Give the power of ten that the decimal must be multiplied by to 
eliminate the decimal point.

   3.825   6.91    19.207

My mom and I can not seem to figure this out.
Thanks, Mike

Date: 10/31/2001 at 12:10:14
From: Doctor Peterson
Subject: Re: Give the power of ten (decimals)

Hi, Mike.

A power of ten is a number formed by multiplying a bunch of 10's 
together, like 1000 = 10*10*10. (I use "*" as the multiplication 

When you multiply a number by ten, you move the decimal point one 
place to the right; for instance

    12.0 * 10 = 120.

    1.2 * 10 = 12.

So if you have to move the decimal point three places to the right to 
make a whole number, then you are multiplying by ten three times, and 
this is the same as multiplying by 1000:

    1.234 * 1000 = 1.234 * 10*10*10
                 = 12.34 * 10*10
                 = 123.4 * 10
                 = 1234.

In other words, just count the decimal places, write that many zeros 
after a 1, and you have the number by which you have to multiply to 
eliminate the decimal point:

   1.234    1000
     \_/     \_/
      3       3

The number 1000 is written as the third power of 10, or

    1000 = 10*10*10 = 10

Does that help?

- Doctor Peterson, The Math Forum   
Associated Topics:
Elementary Place Value
Elementary Square Roots
Middle School Exponents

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