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For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below:

Symbol    Description                                     unit
x         way travelled by the thing                      km
z         fraction of the x and the total possible way    ?

My problem lies in the second symbol "z" which is a dimensionless quantity. I could of course just leave the unit column empty for such quantities, however that would look a bit like there was something forgotten and therefore I would like to indicate somehow that this symbol denotes a dimensionless quantity. Is there a convention to indicate that a unit is dimensionless?

Benedikt Bauer
  • 527

4 Answers4

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Conventionally we use $1$ for dimensionless quantities, although it may cause some confusions. In additon,

The International Committee for Weights and Measures contemplated defining the unit of 1 as the 'uno', but the idea was dropped.

--https://en.wikipedia.org/wiki/Dimensionless_quantity

Qianyi Guo
  • 933
6

Given the way that you've presented your table, I would personally put a "-" rather than a 1 in the units column. This to me would signify that units such as "g, km, s, A" etc. do not apply here. In terms of your symbols, in many branches of physics it is common to use a "hat", "tilde" or "star" notation above a symbol to indicate that it is a dimensionless quantity. For example, if $x$ is the distance travelled and $X$ is the total journey distance, then the dimensionless distance (fraction of the journey already undertaken) could be written as $\hat{x} = x/X$.

If you're interested in dimensional analysis, the you could have additional columns for the fundamental dimensions (Mass, M, Length, L, Time, T, Electric Charge, Q etc.) and indicate the exponent of each dimension with the relevant value, e.g. 

symbol description units M L T
x      distance    km    0 1 0
F      force       kN    1 1 -2
Re     Reynolds No -     0 0 0
Dai
  • 502
3

Yes. In the unit column, put $1$.

Robin Ekman
  • 14,747
2

The only convention I am familiar with is to put a $1$ for dimensionless quantities. If you feel that this could give rise to confusion, you could explain the convention somewhere above or below the table.

RQM
  • 546