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Multiplying and Dividing Decimals

Date: 6/27/96 at 15:0:51
From: Sue Paul
Subject: Decimal Division, Multiplication

Dear Dr. Math,
I am going into Grade 6 next September.  On my report card my teacher 
commented that I have difficulty with multiplication and division of 
decimals.  Would you please explain these concepts?
Thank you, 
    Chris Paul

Date: 7/28/96 at 13:25:1
From: Doctor Robert
Subject: Re: Decimal Division, Multiplication

Hi Chris,

When multiplying decimals you follow this simple rule.  Multiply the 
numbers totally disregarding the decimal points - that is, treat the 
numbers as if they were whole numbers.  Then, after you have done the 
multiplication, count the number of digits to the right of the decimal 
in each of the numbers. ADD these numbers together and then count off 
(from the right) this number of places in the answers and put the 
decimal point there.  

An example will help:

  27.8 x 2.345  

First multiply 278 x 2345 which is 651910.  Now, in the first number 
there is ONE place to the right of the decimal and in the second 
number there are THREE digits to the right of the decimal.  
ONE plus THREE = 4.  Therefore, count four places in from the right of 
the answer.  The answer should be 65.191. 

To divide, you do the following.  Move the decimal point in the 
DIVISOR to the right until the number becomes a whole number.  Move 
the decimal point the SAME NUMBER of places in the dividend.  Then 
proceed to divide the way you would with whole numbers.  The decimal 
point in the answer lies directly above the decimal point in the 

An example:  27.84 divided into 434.6.  Move the decimal TWO places in 
both numbers.  The problem then becomes:  2784 divided into 43460.  
The answer is 15.6106...

I hope that this helps.

-Doctor Robert,  The Math Forum
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Associated Topics:
Elementary Fractions

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