Let me give my input to the confusion :-)
Things that can be counted are integers, and have no unit. They may,
however, have a _nominal_ unit, which can be "stripes", "apples",
"pieces of fruit". Those units are solely used for clarity. For
example, I can have 13 pieces of fruit, but that may be 5 oranges and
8 bananas, or 12 apples and 1 kiwi, so to avoid confusion, I'd better
name those units; they become nominal (nomen == name).
Some things cannot be counted. Like the height of the tree outside my
window. I would say its height is 12, and Dale would say its height is
37. The height of the tree is a continuous variable, and so it needs
to be measured in some unit. Therefore, the height of the tree can't
be specified as just "12"; it is indeed "12 m" or "37 feet".
It so happens that we think of electrons as particles, so on one hand,
you might imagine that you can "count" electrons. We can argue whether
or not that is true; someone might claim that electrons are
delocalized, and can only be positioned via some kind of probability
function. Perhaps it would make more sense to count the number of
protons in the atomic nucleii of the unit cell, since those are used
to compute the number of electrons anyway.
I always enjoy asking students what the unit of an equilibrium
constant is, and they always answer "molar" or "micromolar squared" or
"milimolar to the minus first" ... etc. That is of course wrong;
equilibrium constants are dimensionless, but are almost always given
nominal units for clarity, especially by biologists.
Cheers,
Morten
