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You probably know that in math, English-speaking folks talk about positive numbers, negative numbers, real numbers, complex numbers, irrational numbers, etc. Doing so, they are talking about classifications or kinds of numbers, not any particular set of digits and decimal points. If I were to rewrite the last two sentences in German, I would not use the word Nummer or its plural. I would use Zahl and its plural
. And in English I could write that that the division of the number 4 by the number 2 gives a quotient equal to the number 2, again using the word number. And if I were to rewrite that in German, I would use the word Nummer, not Zahl.
you would say: "Die Division der Zahl/des Wertes 4 mit der Zahl/mit dem Wert 2 ergibt die Zahl/den Wert 2" - usually I would use Wert or omit the word ("Die Division von 4 und 2 ergibt 2") but 27.50 is a Nummer
It is a Wert or a Zahl in case of calculations, ... whether it is my home address, my grocery bill total, my age or the number of times I've tried to understand the difference between Nummer and Zahl.
It depends. It is a "Nummer" in the most of the cases. A Nummer is a kind of Zahl but not every Zahl is a Nummer. Whether or not it makes mathematical or common sense in a particular context to perform arithmetic operations with 27.50 (square it, cube it, take the arc tangent of it) is irrelevant; 27.50 is a Nummer.
It is not a Zahl. So, I believe, that if one writes "The U.S. unemployment numbers...", and wants to translate that into German, Zahlen would be the appropriate word to use for "numbers."
this is correct, but usually we say "die Anzahl der Arbeitslosen" rather than "die Zahl der Arbeitslosen." But if he/she wants to translate "The U.S. unemployment rate is above 9%", that 9 is a nummer, not a Zahl.
in this case I would use "Wert", but a Wert is a Zahl. A Wert is usually not a Nummer. (May be in some context, but at the moment I cannot imagine.) Again, I realize that this reply is not complete. But I hope it clarifies one small corner of the question.