Multiplication of Decimals

Date: 01/02/2002 at 11:03:43
From: Emma
Subject: Multiplication of Decimals

Find the value of 36.5 x 3.504.

I ignored the decimals and worked out the answer and discovered that 
when the numbers after the decimals are added together, the decimal 
point can then be placed that number of places from the right. 

For example, the total number of decimal places moved for the sum 
above is four, and I know the answer is 1278960 and when the decimal 
point is placed the answer will be 127.8960. But I don't know why or 
how it always works. Can you please help me?

Many thanks.

Date: 01/04/2002 at 02:31:38
From: Doctor Ann
Subject: Re: Multiplication of Decimals

Dear Emma,

Thank you for writing to Dr. Math. You have asked a good question. I 
hope this explanation helps:

Let's re-write your problem:

     36.5 x 3.504 = 365 x (.1) x 3504 x (.001)  

(Do you agree with this?)

Now use the commutative law to rearrange to:

                  = 365 x 3504 x  (.1) x (.001)  

                  = 1278960    x   (.0001)   

(Do you recognize this?) 

I hope that from this you can see why you can "ignore the decimals and 
work out the problem" and then adjust the decimal point for the final 
answer.

If you have another question, please feel free to write to Dr. Math. 

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