stellige

Stellige is a German mathematical term referring to the number of digits used to write a number in a given base, most commonly base 10. In everyday German mathematics education, numbers are described by phrases such as einstellige Zahl (one-digit number), zweistellige Zahl (two-digit number), dreistellige Zahl (three-digit number), and so on. The adjective stellige or the compound forms like einstellige, zweistellige, dreistellige modify the noun Zahl or Ziffern to indicate digit length.

Formally, a positive integer n has k digits in base 10 if 10^(k-1) ≤ n ≤ 10^k − 1. By convention, zero is usually treated as a one-digit number since it consists of a single numeral. The concept generalizes to any base b ≥ 2: a k-digit number in base b satisfies b^(k-1) ≤ n ≤ b^k − 1. In texts, you may encounter terms such as einstellige Zahlen or mehrstellige Zahlen to distinguish single-digit numbers from those with more digits.

Relation to other concepts includes the digit-count function and logarithms: the number of digits of n in base 10 is floor(log10(n)) + 1 for n > 0. This approach also explains why powers of 10 mark the boundaries between digit lengths (e.g., 9, 10, 99, 100, 999, 1000).

Common usage aside from German education appears in discussions of number sizes, rounding, and algorithmic digit processing. The concept remains a straightforward way to classify integers by their length in a chosen numeral system. See also digit, base representation, and logarithmic digit counting.