Re: [Phys-L] unit for "pure ratio"

[Robert Cohen <Robert.Cohen@po-box.esu.edu>]

On Sunday, July 24, 2016 1:10 AM, John Denker [jsd@av8n.com] wrote (among other things):

> Background:  When something is dimensionless, that doesn't mean it is
> unitless.  For example, angles can have units of cycle, radian, degree,
> milliradian, et cetera.

> Also ratios can have units of percent, ppm, et cetera.

Or ratios can be written without any of those units you mention.

The question, then, is what do you call the unit when no word or symbol follows the number?

I think it is simpler just to call that a case where "no unit" is used. In other words, dimensionless doesn't *necessarily* mean it is unitless but it *could* be.

> The best I've seen so far is /perun/ which comes from Latin "per unum"

So a coefficient of friction equal to 0.5 perun is equivalent to a coefficient of friction equal to 0.5?

If so, what is it that has been left off the latter?  The unit name?  So the unit is still there but the name of that unit is left out because we don't need it?

And so a dimensionless number is not unitless but it can be unit-name-less?

------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University
East Stroudsburg, PA 18301
________________________________________
From: Phys-l [phys-l-bounces@www.phys-l.org] on behalf of To: Forum for Physics Educators
Subject: [Phys-L] unit for "pure ratio"

Hi Folks --

Question:  Is there a good name for the unit when something is measured
as a pure ratio?  This unit would be hundred times bigger than a percent,
and a million times bigger than a ppm.

Such a unit would come in handy for lots of things where there is a
ratio that happens to be on the order of unity.  Common examples include:
 -- aspect ratio
 -- coefficient of friction
 -- coefficient of lift
 -- et cetera.

in analogy to percent ("per centum").  So if we use metric prefixes,
a percent would be a centiperun, and a ppm would be a microperun.
This is discussed at
  http://aakilfernandes.github.io/perun-a-useful-unit-for-dimensionless-programming
  https://www.reddit.com/r/ethereum/comments/3tzuwu/perun_a_useful_unit_for_dimensionless_programming/
  http://stats.stackexchange.com/questions/215942/percent-describes-per-100-what-term-is-used-to-describe-per-one-as-in-probabi

Does anybody know of anything better?
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