Stellzahl

Stellzahl is a German term used in mathematics to refer to a digit within a numeral in a positional numeral system. Each Stellzahl occupies a position, or place, in the representation of a number, and its numerical value is determined by both the digit itself and its place value (Stellenwert). The Stellzahl is the digit, while the Stellenwert is the weight assigned to that digit, typically a power of the base of the numeral system. In the decimal system, for example, the weights are powers of 10.

In the decimal number 5,483, the Stellzahlen are 5, 4, 8, and 3. The leftmost 5 lies in the thousands place and has a Stellwert of 1000; the 4 is in the hundreds place with Stellwert 100; the 8 in the tens place with Stellwert 10; the 3 in the ones place with Stellwert 1. This illustrates how a number is the sum of its Stellzahlen times their respective Stellwerte.

Stellzahl is sometimes used in German educational contexts to refer to the digits of a number, in contrast to Ziffer, though the terms are largely synonymous. In contemporary usage, Ziffer is more common, while Stellzahl emphasizes the digit’s role within the place-value system.

In other base systems, the same concept applies: a base-b numeral uses digits 0 through b−1; the Stellzahlen with their corresponding weights sum to the value of the number. The concept of Stellzahl is thus central to the understanding of place value in arithmetic and computer science.

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