Back to the subject of unit conversions... there are a couple things I
have found helpful with some students.
First, I think explicitly writing down the string of conversion factors
(unit multipliers) helps.
Second, I think it helps to use the power-of-ten prefixes in front of
the base unit. Let me explain this with examples.
I am not sure where they get this from, but students have an inclination
to think 1000 mm per meter rather than 10^-3 m per millimeter. This
means when they write down (1000 mm)/(1 m) they are making a mental
decimal shift. Had they written (1 mm)/(10^-3 m) they are only
remembering that milli is 10^-3.
As an example I've used an experimental result in (picofarad-millimeter
per square-centimeter) that needs to be converted to (farad-per-meter).
If the student multiplies this by ...
(1 F/10^12 pF)*(1 m/1000 mm)*(100 cm/ 1m)^2
it works. But students will sometimes get the number inverted, and the
also get confused by the square. I prefer...
(10^-12 F / 1 pf)*(10^-3 m / mm)*(1 cm / 10^-2 m)*(1 cm / 10^-2 m)
It's not a "cure-all" but it helps some students.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu