PlatzwertSysteme

A Platzwertsystem, or positional numeral system, is a method of writing numbers where the value of a digit depends on its position within the numeral. This is in contrast to non-positional systems, where each symbol has a fixed value regardless of its placement. The most common example of a Platzwertsystem is the decimal system (base-10), which uses ten digits (0-9). In the decimal system, the number 321 means 3 hundreds, 2 tens, and 1 one. The digit '3' represents 300 because it is in the hundreds place, while if it were in the tens place, it would represent 30.

Other Platzwertsysteme exist, such as the binary system (base-2) used in computing, which employs only two digits (0 and 1), or the hexadecimal system (base-16), which uses digits 0-9 and letters A-F. The concept of a zero or a placeholder symbol is crucial for effective Platzwertsysteme, as it allows for the representation of numbers with gaps in certain place values, such as the number 102 in the decimal system, where the zero indicates the absence of tens. The development of Platzwertsysteme revolutionized mathematics and facilitated complex calculations.