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I'm searching for a unified name to convey for the concept that a number will always be between zero and one.

Some info for context:

in probability we've got a number between 0 and 1. Percentages appear to be similar in that we've got a number between zero and one, but it is multiplied by one hundred.

The nearest names that I've got so far are "factor" or "coefficient", but both of these names could be larger than 1, or smaller than zero.

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Percentages don't have to be between 0 and 100. –  Qiaochu Yuan Sep 1 '11 at 5:14
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Such rationals are precisely the positive proper fractions. –  Bill Dubuque Sep 1 '11 at 5:19
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@Bill: maybe that should be an answer? –  J. M. Sep 1 '11 at 5:45
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You could call it a probability. But you should decide whether you are talking about rational numbers (as in the title) or any old number (as in the 1st line of the body), and then edit accordingly. –  Gerry Myerson Sep 1 '11 at 5:46
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math.stackexchange.com/questions/2489/… seems related, but I am not sure if this question is a duplicate. –  Srivatsan Sep 1 '11 at 14:07
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2 Answers 2

up vote 6 down vote accepted

The rationals in the unit interval are known as positive proper fractions. For a real number $r > 0$ its fractional part is $\:\{r\}\: :=\: r - \lfloor r\rfloor\:.\ $ (I moved this comment to an answer per requests)

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Since the mantissa of a logarithm is a value between 0 and 1 (I'm just barely old enough to have used logarithm tables instead of calculators in high school) I thought maybe googling "mantissa" might suggest something (and if not, I was still going to suggest something like "a mantissa number" for a number between 0 and 1), and when I googled, I immediately found the following at Wolfram's Mathworld site:

http://mathworld.wolfram.com/Mantissa.html

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Huh. The use of mantissa I'm accustomed to would have the $9.2361$ in $9.2361\times 10^5$ be the mantissa. I guess it depends... –  J. M. Sep 1 '11 at 14:03
    
@J.M. To me, mantissa meant what you are thinking of as well, but the two mantissas seem to be related by the scientific notation/logarithms. (Useful fact: $9.2361 \times 10^5 = 10^{5.9655}$) The Dave-mantissa of $5.9655$ is $.9655$, which is the log of our mantissa $9.2361$. –  Srivatsan Sep 1 '11 at 14:18
    
@J.M.: Now that you mention it, your use of "mantissa" is how the word was used when I was in school. The mantissa is the part of the number you look up the logarithm of in logarithm tables. I don't think we ever called the logarithm of what we looked up a "mantissa", despite what my apparently fading memory initially had me thinking. –  Dave L. Renfro Sep 1 '11 at 15:37
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I regret that I didn't think of naming my daughter Mantissa. A lovely name, don't you think? –  Gerry Myerson Sep 2 '11 at 2:00
    
I'll mull over the mantissa suggestion. For some reason that word is tied to scientific notation for me. Perhaps there's a useful more general use of the work too. –  sgtz Sep 5 '11 at 9:19
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