Converting Units of Measure

Date: 7/17/96 at 17:2:19
From: Anonymous
Subject: Unit of Measure

Dear Dr. Math,
 
Could you please explain to me what Factor Analysis is and what it 
means?  In my Algebra II book I have the following question: "Find the 
unit of measure for the product and explain your reasoning.  
(3 pounds over 1 square inch) (144 square inches over 1 square foot) 
(1 ton over 2000 pounds) ($25 over 1 ton)." I would greatly appreciate 
it if you sent me the answer and a description of how you got it, 

Thanks,
        Daniel   

Date: 7/21/96 at 20:7:6
From: Doctor Robert
Subject: Re: Unit of Measure

I am not sure that I know exactly what your book means by Factor 
Analysis, but I think I understand your question. The problem arises 
when you must convert a quantity expressed in one set of units to an 
equivalent quantity expressed in a different set of units. 

Perhaps an example is the best way to explain it. Suppose that you 
know the speed of a snail in inches/day and that someone wants to know 
the snail's pace in mi/hr. You can multiply the snail's speed by any 
fraction that is really one. For example 12in/1 ft is really just one 
because there really are 12 inches in a foot.  60min/1hr is really 
just one because there really are 60 minutes in an hour.  So, suppose 
that the snail's pace is 14 inches/day.  To convert this to mi/hr I 
would multiply by a succession of fractions equivalent to one.  

The calculations follow:

(14 in/day)(1ft/12in)(1 mi/5280 ft)(1 day/24 hr)= .00000921 mi/hr.

If you write each fraction with a horizontal fraction line you can see
that all the units cancel except the final ones in the answer. In 
other words, you can cancel units just like you do factors when 
dealing with fractions. 

I hope that this helps.

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/