Writing Quantities and Variables the Correct Way

I researched on how to write units, constants and quantities, and variables the proper way. There’s a lot of information out in the interwebs. And, of course, not everything is correct.

In 2010, a new ISO standard was published, the ISO 80000-2, describing mathematical signs and symbols. You can buy it here (buying a ISO paper, it’s strange, right?).
There’s a LaTeX package called isomath implementing this standard for your favorite typesetting tool.

Following some notes from it on upright-edness and italic-ity.

  • Units are to be written upright (roman). Capital, when they are based on names (K for Kelvin), small when not (m for meter). See more on that at Andrés blog.
  • Variables are to be written in italics (slanted), independently if the character is latin or greek. x = 12, α = 1.
  • Mathematical constants are to be written upright. Physical ›constants‹ in italics.
    π is upright, so is i as in i2 = -1.
    In italics is the speed of light, c, the Avogadro constant, NA.
  • Well-known functions are upright, like sin x or exp x.
    And this means, yes, also the the e in e2x is upright, as it’s both a function and a mathematical constant.
  • Indices of variables are upright when they are descriptive. See the Avogadro constant above.
  • Differential operators are upright, but not the variables/quantities they differentiate (for). dx/dt.
  • Particle name abbreviations are upright. Independently if it’s a latin letter (the electron’s e) or a greek one (the pion’s π).

While we are at it: The correct way to describe axes in plots is to state the measured variable (e.g. ρ), state a slash as a division sign (/) and then the unit of the variable (e.g. MPa) – ρ/MPa1. The order of variable and unit can be interchanged if the value given is reciprocal, e.g. 1/ρ would lead to a description of MPa/ρ. Writing square brackets for the unit is not correct (as in [MPa]).

Ressources I used to compile this list, sorted by importance:

  1. Think about it: Every quantity ρ on the axis is divided by the unit, hence the number essentially loses its dimension, as shown on the axis. 

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  1. Pingback: How to correctly write units in texts | dr.andre

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