bug#13580: 24.2.92; regression in calc-convert-units

[Eli Zaretskii]

> From: Jay Belanger <jay.p.belanger@gmail.com>
> Date: Thu, 07 Feb 2013 15:11:58 -0600
> 
> I've been consistently talking about units, not dimensions; I have given
> no interpretation of "dimensions" vs "units".  The expression above has
> no units when simplified; that's a pretty straightforward statement.

He is talking about this (see
http://en.wikipedia.org/wiki/Dimensionless_quantity):

  In dimensional analysis, a dimensionless quantity or quantity of
  dimension one is a quantity without an associated physical
  dimension. It is thus a "pure" number, and as such always has a
  dimension of 1. [...]

  Even though a dimensionless quantity has no physical dimension
  associated with it, it can still have dimensionless units. To show the
  quantity being measured (for example mass fraction or mole fraction),
  it is sometimes helpful to use the same units in both the numerator
  and denominator (kg/kg or mol/mol). The quantity may also be given as
  a ratio of two different units that have the same dimension (for
  instance, light years over meters). This may be the case when
  calculating slopes in graphs, or when making unit conversions. Such
  notation does not indicate the presence of physical dimensions, and is
  purely a notational convention. Other common dimensionless units are
  % (= 0.01),  ‰ (= 0.001), [...] and angle units (degrees, radians, grad).

Therefore, "dimensionless" and "unitless" is not the same, and you see
above prominent examples of such dimensionless units.

IOW, removing dimensions of an expression as part of simplifying it
might sometimes lose information.  E.g., dividing the length of a
circular arc by its radius will give you m/m, but the natural units of
this are radians or degrees, not lack of units, and talking about
"unitless" in this case might make little sense to a user who _knows_
she is computing an angle.