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Re: [Phys-l] Unit Conversions (was Mass and Energy)

Hmmm. Actual talking about actual unit conversions in this thread. Hmmm.

Al Bachman wrote:
I blame textbook authors and publishers for part of the problem.
The usual practice is to use "conversion factors" so as to be able
to write a conversion on a single line and eliminate the writing of
the individual equivalences that are used.

For example, the conversion of 1 m to inches might appear as

1 m ( 100 cm/ m)( 1 in/ 2.54 cm) = 39.37 in [1]

[ the fractions would appear with horizontal fraction lines,
and the cancelled units with slashes. ]

This practice also presents what is essentially a multi-step problem
( a notorious challenge to weak students) as a single step.

The factor-label method (equation [1] above) can easily be re-written
as a sequence of steps.

Let's be clear: The multi-step observation is valid, and the
textbooks can be properly criticized for jumping too far ahead ...
but it strikes me as unfair to tar the factor label method with
this brush.

I fully endorse Robert Cohen's approach of "unit replacements"

I see it as six of one and half-a-dozen of the other. I see no
strong arguments either way. Use whatever you like, or use
whichever works best on a student-by-student basis if you've
got that kind of time.

To amplify on that approach, the basic idea is to
"treat the units abbreviations as algebraic symbols",

The usual factor-label method does exactly that.

and to do one conversion at a time.

The usual factor-label method can be done that way, no problem.

The above conversion might then look like:

1 m = 1 (100 cm) = 100 cm
1 in = 2.54 cm

so cm = in / 2.54

100 cm = 100 (in /2.54) = (100/2.54) in = 39.37 in

In this format it is easy to scan up and down to check the steps.

Yes, but "(in/2.54)" in the middle part has to be checked against
the "cm" on the LHS. This requires more eye-strain and is a less
obvious form of checking that is involved in equation [1], where
each of the parenthesized factors can instantly and *locally* be
verified as equal to unity.

Again: there are reasonable arguments on both sides. Both methods
are reasonable methods. De gustibus non disputandum.