Anthony Lapinski and Bernard Cleyet have commented on the failure of the
USA to go metric, thereby forcing students to spend time on unit
conversions and distracting them from the physics. Ludwik Kowalski
commented that he considers units consisting of an SI unit prefaced with
a multiplier such as centi-, kilo-, milli- are still SI units.
The "metric system" does not solve the problem, and centimeters,
picofarads, kilometers are not SI.
It was implicit in my original post that students have difficulty
converting from milliseconds to seconds. They find this every bit as
difficult as converting from inches to meters. You may say, yes but at
least the ms-to-s conversion doesn't require the students to look up a
conversion factor. I wish that were true. There are two problems. (1)
Even though I tell students to memorize the power-of-ten prefixes from
pico to tera, and I tell them the names, abbreviations, and numbers will
be on the first exam, over half the class will miss some of these on the
exam. One or two weeks after the exam it is almost as if I never told
the students to learn these. (2) Even if the student remembers that
milli is one-thousandth rather than one-millionth, they still have
difficulty in a conversion as to whether they divide by 1000 or multiply
by 1000. Moving the decimal point is no more easy than multiplying or
dividing by 2.54 cm/in.
I am sad and embarrassed to tell you that I mostly deal with college
sophomores taking calculus-based physics. These are biology, chemistry,
physics, computer science, pre-med, pre-science-teacher students. They
absolutely cannot do metric-to-SI conversions any more readily than
USA-to-SI.
Here is an example...
Using a movable-plate parallel-plate air-dielectric capacitor they
measure capacitance in picofarads as a function of plate separation in
millimeters. They plot capacitance as a function of inverse-separation
to get a straight-line plot with slope of [plate-area times
permittivity-of-air]. Of course in SI units the permittivity of air is
about 8.85E-12 farads-per-meter. The slope of their graphs, if they
keep their data units, has units of picofarad-millimeters. They measure
the plate diameter with a calipers reading centimeters, so their plate
area is in units of square-centimeters. The permittivity is slope
divided by area, and their result comes out in units of
[picofarad-millimeter per square-centimeter]. How many students can
convert this to farads-per-meter without my help? In the second
semester of their sophomore year, fewer than half of my students can do
this without a trip into my office to help them find out why they are
off by several orders of magnitude. It is truly sad.
What's the problem? (a) forgetting that pico is 10^-12, milli is 10^-3
(rather than 10^-6), centi is 10^-2 (rather than 10^+2), centimeters^2
would be 10^-4 meters^2 rather than 10^-2. (b) mixing up division and
multiplication; that is, multiplying by an upside-down conversion
factor.
Perhaps worse (more comical?) is the student who has poor data, does the
unit conversions correctly, gets a permittivity of 1.02E-11 F/m, and
wants to know why they are off by a factor of ten.
Anyway, "going metric" won't help this kind of problem.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu