Multiplying Decimals and Decreasing Answers

Date: 12/02/98 at 21:32:14
From: Danny Graham
Subject: Multiplying decimals

I know that when I multiply, .60 * .75 * .80 = .36.

But what is the .36 telling me? 36/100. It seems I have less than I had 
when I started.

I read the questions others have asked, and I understand the process 
of multiplying the decimals, I just don't understand what the answer 
is telling me.

Thank you,
Danny Graham

Date: 12/03/98 at 17:57:53
From: Doctor Rick
Subject: Re: Multiplying decimals

Hi, Danny. I'm impressed - you're really thinking! Multiplication isn't 
just a set of rules you follow to please the teacher. It's supposed to 
tell you something. So, what is it telling us?

It is surprising indeed that multiplication can give you a smaller 
number than you started with. One student from a foreign country got 
really upset at this - his foreign-language dictionary told him that 
"multiply" is a synonym for "increase," so how can it make numbers 
decrease?

Numbers decrease when you multiply by a number less than one. It works 
the same with fractions as with decimals. For instance, if you multiply 
any (positive) number by 1/2, the answer is less than you started with.

Let's rewrite your decimal multiplication problem as fractions:

  .60 * .75 * .80 = .36

   3     3     4     9
  --- * --- * --- = ---
   5     4     5     25

The answer comes out the same, if you work it out: 9/25 = 0.36. The 
only new thing is that it is much easier to see that 0.36 < 0.60 than 
it is to see that 9/25 < 3/5. (It is: 3/5 = 15/25, and 9 < 15.)

Multiplying by a decimal less than 1 will always decrease a number.
Multiplying by 0.75 is the same as multiplying by 3/4, and 3/4 of 
something is always less than 4/4 of it, which is the whole thing. 

I hope this helps you to see what is going on.

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