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So in my math class, the solution for finding the standard divisor is:

20,000 / 18 = 1, 111.111111

The class round it to the whole number, so 1,111. We still get the same number of representatives and standard quota. Our reason for using the whole number is due to the fact we're dealing with people. There are no fractional numbers when it comes to dealing with people. However, she marked it wrong and said she wanted it as 1, 111.11 because she wants to copy everything in the calculator but its missing 4 more decimal places. -_-

So should standard divisors be whole numbers when it comes to dealing with people or no?

Jyrki Lahtonen
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Jem
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    The only context in which I have seen the term "standard divisor" is in the apportionment of representatives, as here for instance. But there's no rounding involved, there...one works with the fraction as it stands. Is this what you are talking about? – lulu Sep 13 '18 at 23:18
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    Stating the original problem would help users understand the context in which the number of decimal places is being determined. – N. F. Taussig Sep 13 '18 at 23:19
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    Welcome to math.SE. Please don't shout in the titles. Thanks. – joriki Sep 14 '18 at 04:11
  • Traditionally the dividend is divided by the divisor to get a quotient, possibly with a remainder – Henry Sep 14 '18 at 05:44

1 Answers1

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The standard divisor should not be rounded. It does not represent a number of people which you are going to use as a final answer to a question in which a fractional person would be meaningless. It is instead an intermediate stage in the calculations which will be plugged into later calculations. Rounding the standard divisor will make those later calculations (of the standard quotas) inaccurate.

To put it another way, the standard divisor represents the average number of people per seat. There is no reason for an average to be an integer, even if it is an average of integer quantities. For instance, the average household in the US has about $2.6$ people. Obviously there are no actual households that have exactly $2.6$ people, but some households have $2$ (or less) and others have $3$ (or more) and it ends up averaging out to $2.6$.

Eric Wofsey
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