Take the tour ×  In the Talk page of Wikipedia Coefficient I
read this comment:  As far as I can tell, the mathematical
definition should imply that coefficients are unitless, however,
the physical sciences have been using "coefficient" for factors
that include dimensions for a long time, where "constant" or
"factor" would be a more informative term.  In the same page,
examples of "physical coefficients" have both dimensionless and
dimensionful coefficients. I am trying to understand the
difference of how "coefficient" is used in mathematics and
physics.   share|improve this question Assigning units to
mathematical constants can be a useful way to find errors.
Taking the quadratic $ax^2+bx+c=0$, if you imagine $x$ having
units of length then $a$ must be length$^{-2}$, $b$ must be
inverse length, and $c$ must be unitless. This would catch
certain errors in the derivation (or memory) of the quadratic
formula. It won't catch all errors, but neither does casting out
$9$'s. –  Ross Millikan Jan 14 '12 at 5:29 add