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I'm building a units based type for C++ which describes probabilities (using boost::units library.) While I know that the values of probabilities are dimensionless, I think it makes some sense in the same way that angles (another dimensionless quantity) are often given units. My question is given that percent is a reasonable unit for parts per 100, is there some such concept for parts per unit/one? Following the etymology of percent (from per centum) I arrived at per unus (latin for one) => perun. However, I would prefer not making one up.

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  • $\begingroup$ Please give an example sentence where you would want to use this term. $\endgroup$
    – amoeba
    Commented Jun 2, 2016 at 13:11
  • $\begingroup$ proportion? fraction? probability? $\endgroup$
    – Glen_b
    Commented Jun 2, 2016 at 15:24

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  • Proportion or fraction (if out of one) or percentage (if out of 100) seem pretty innocuous and easy to interpret. Other bases may work too, like parts-per-million, depending on your intended domain. For example, some fields report outcomes as X per 100,000 patients or parts per million.

  • You could label them as relative frequencies (or something like r_freq), though this (obviously) has an frequentist slant and might be a little bit odd if the probability is being used to describe something like a degree of belief. On the other hand, if you're explicitly encoding subjective beliefs, you could call them credences (or maybe cred for short).

  • There isn't anything weird about calling the units probability, in the same way we often label an angle as being "in radians" even though angles are, in fact, dimensionless.

  • You could coin your own term, though I have a strong but viseral dislike of "perunus"--it just looks weird. It's emtymologically tempting, but I would strongly suggest not overloading probit either--it's confusing.

  • In some situations, it might be more natural to use odds instead of probability, which you could label as odds or odds ratio. I suppose there's also the Hartley or ban/deciban too, though these aren't quite probabilities (and have a very old-fashioned, Bletchley-park sort of feeling to them).

Finally, make sure that you're distinguishing between probabilities (which are dimensionless) and probability densities, which have units of $\frac{1}{\text{whatever}}$ (and, obviously, may be larger than one).

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I usually use the term "proportion".

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    $\begingroup$ Fraction also works $\endgroup$
    – wabbit
    Commented Jun 2, 2016 at 13:30
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A percent is just another way to represent any fraction by scaling it to be out of 100. You could do this for your scenario since something like .25/1 is obviously 25% of 1. It seems like there isn't a special term since there doesn't need to be.

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