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Re: dimensionless units



One thing remains clear to me... this radian stuff does confuse the
students. Several of you have confirmed this. As I have read through the
postings on this topic my goal has been to figure out a way to help
students. I think several of you have helped me. Here's my current
thinking:

(1) Several have disagreed with my practice of just leaving radians out.
Okay, I think you have convinced me.

(2) John Denker says to "throw them away" when you do dimensional analysis
by noting they are a dimensionless unit. Okay. I buy that also. But
that's where the students have the problem. They aren't used to
dimensionless units. They don't have a feel for when to throw things away
or keep them.

(3) Joel Rauber suggests using Mach number as another example of a
dimensionless unit to help students get used to this idea. Analogies are
always good, but Mach number strikes me as even more obscure than radians,
i.e. the students are not used to it.

(4) Bernard Cleyet pointed out some interesting aspects of %. This got me
wondering if percent might be a good example of a "throwaway" word.

If a student did a calculation and used a mass of 3.0 kg, then we suggested
to do the calculation again but multiply the mass by 50%, they would not
multiply 50% times 3.0 kg and come up with 150.0 %kg [alas, some would, but
most would not]. Or thinking in reverse, they know that 1.5 kg / 3.0 kg is
0.5 (dimensionless) but we multiply by 100 and tack on percent and call it
50%.

Maybe that's not a great example, but it illustrates the idea that some
things, like percent, yield symbols or units that have to be thrown away or
otherwise manipulated in the appropriate way at the appropriate point.

John gave a list of a few of these dimensionless units. Is that an
exhaustive list? Can others think of better or other examples?

Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817