Multiplying by a Decimal Number

Date: 02/28/2001 at 14:34:14
From: Carolyn Trancovich
Subject: Multiplication of decimal numbers

I am having trouble understanding why multiplying by decimal numbers 
gives a product smaller than the factors. For example, 5 * .43 = 2.15.  
I just always thought that multiplying would make the product bigger 
than the numbers I used.  

Thank you.

Date: 02/28/2001 at 16:49:42
From: Doctor Rick
Subject: Re: Multiplication of decimal numbers

Hi, Carolyn.

When you only knew about whole numbers, you could make a rule like the 
one you stated - but not quite! Even when you only knew about whole 
numbers, there was one exception to your rule: multiplying by 1 does 
not make a number bigger. When you added zero, that was another 
exception.

If you multiply by a number greater than 1, the product will be 
greater than what you started with. If you multiply by 1, the product 
is the same as what you started with. If you multiply by a number less 
than 1, the product is less than what you started with.

Let's make some sense of this by considering a simple example. 

Multiplying by 1/2 is the same as dividing by 2. Do you understand 
this? Multiplying by 1/2 means taking half of it; dividing by 2 means 
cutting it in two pieces and keeping one. These amount to the same 
thing. Since 1/2 = 0.5, and half of something is less than the whole, 
it makes sense that multiplying a number by 0.5 makes it smaller.

You've asked a good question, and others have wondered about it, too. 
Here are some answers I have written to other students on this topic:

  Multiplying Decimals and Decreasing Answers
  http://mathforum.org/dr.math/problems/graham12.2.98.html   

  Multiplying by 1
  http://mathforum.org/dr.math/problems/abbasi9.1.98.html   

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