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When talking about positional notation, is there a technical term for "place-value" (as in, "the place-value of the 9 in 792 is 10), or is that it? Somehow, "place-value" sounds informal, but I don't know that I've heard an alternative ("magnitude" seems close, but it's more general).

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  • $\begingroup$ One term is positional notation. You may also encounter radix notation. $\endgroup$ – Brian M. Scott Feb 28 '16 at 21:47
  • $\begingroup$ Just to be clear, there's the power of the $N$ by which you multiply each digit in a base-$N$ number, and there's the entire idea of "base-$N$". Either one of them might be called "place value"; are you specifically asking about the first kind of "place value" (the power of $N$ at a particular place in the numerical representation)? $\endgroup$ – David K Feb 28 '16 at 23:41
  • $\begingroup$ @DavidK Yes, I'm asking about the first, as in, "the place-value of the 9 in 792 is 10" $\endgroup$ – ivan Feb 28 '16 at 23:55
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It may be that "place value" is the best specific technical term you will find. It seems to be commonly used by mathematicians; for example, as far as I have been able to determine, the entire entry on Positional notation in Wikipedia, consistently uses "place value" when explaining the structure of a numeral in positional notation, and nobody has inserted any clear alternative terminology. I do not recall seeing any other terminology elsewhere, either; if the term "place value" does not sound "serious" enough, it may be because most "serious" mathematics does not depend on literal numerals being written in any particular way, provided it is clear what their values are.

If you want to sound a little more formal, you might write "order of magnitude" for the power of the base by which each digit is multiplied, but order of magnitude is a more abstract concept that does not necessarily correspond to place value in whatever positional number system you are using. It just happens that the place values of digits in a positional system are equal to orders of magnitude, provided that the positional system and the orders of magnitude use the same base.

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