Metric Unit Conversions

Date: 08/21/2001 at 21:59:26
From: Damian Montgomery
Subject: Changing metric units

How do you know when you should multiply or divide in these 
conversions?

Date: 08/22/2001 at 14:20:18
From: Doctor Ian
Subject: Re: Changing metric units

Hi Damian,

Actually, when converting units, you're always multiplying by 1 (which 
is why you can do it without changing the meaning of anything).  For 
example, 

          
         1 in       1 ft   
  3 cm * -------- * ------ = ?
         2.54 cm    12 in    
          
            ^         ^
            |         |
         This is    So is this.
         the same
         as '1'. 

Note that you can treat the units just as if they were numbers; and 
since the order of multiplications is irrelevant, you can group them 
all at the end

         1 in       1 ft     3 * 1 * 1   cm * in * ft
  3 cm * -------- * ------ = --------- * --------------
         2.54 cm    12 in    2.54 * 12   cm * in
          
Once they're grouped like that, you can cancel them, just as you would 
cancel numbers that appear in both the numerator and denominator of a 
fraction:

                                         x    x
         1 in       1 ft     3 * 1 * 1   cm * in * ft
  3 cm * -------- * ------ = --------- * --------------
         2.54 cm    12 in    2.54 * 12   cm * in
                                         x    x


                           = 3 / (2.54 *12) ft

So, when you need to convert something, how do you decide whether to 
multiply by 

  21.2 blurgs
  -------------
  0.015 zibbles

or 

  0.015 zibbles
  -------------      ?
  21.2 blurgs

The answer depends on which unit you need to cancel. If you're 
starting with zibbles, the first one will give you

  zibbles * blurgs
  ----------------
  zibbles

which is the same as blurgs; but if you're starting with blurgs, then 
the second one will give you

  blurgs * zibbles
  ----------------
  blurgs

which is the same as zibbles. 

Does this help?  Let me know if you'd like to talk about this some 
more, or if you have any other questions. 

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