Q&A #1834

Dimensional analysis of measurements in Metric system

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From: Jenny (for Teacher2Teacher Service)
Date: Aug 06, 1999 at 14:36:11
Subject: Re: Dimensional analysis of measurements in Metric system

Hi Stephanie - when I teach changing units, I include dimensional analysis
as one of the ways to do it.  I think the key is to relate the process back
to concepts the students are familiar with - in this case proportions and
multiplying by 1, because that's what you're really doing when you multiply
by the conversion factor.  For example, suppose I need to change 254 cm to m.

My conversion factor is

   1 m
________ .  Kids always wonder why I picked this form.
  100 cm

I model it by thinking out loud:  "I need 2 equivalent measurements (so the
fraction equals 1) that contains cm and m.  I know 1 m = 100 cm and I need
the cm in the denominator so the cm units will be the fraction 1 (divide
out).  I need to check that I'm using a conversion that really equals 1 and
that I'll get m left when I divide everything."

            1 m           254 cm x 1 m     254    cm     m
254 cm x   ------     =  --------------  = --- x --- x ---
           100 cm          100 cm          100    cm     1

=  2.54 m

If you haven't tried modeling the process out loud and relating it back to
multiplying by 1, you might try this.  It usually works for my students.

 -Jenny, for the Teacher2Teacher service

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