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How do numerals represent numbers in different writing systems?

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Two vertical tablets display ancient symbols for the numbers one and ten from Egyptian hieroglyphic, Egyptian hieratic, Sumerian, and Cretan scripts, with each symbol shown in red next to its culture and approximate date. — numerals and numeral systems Examples of ancient symbols for the numbers 1 and 10.

Numeral systems represent numbers through sets of symbols and specific rules for their application. These systems generally fall into two categories:1

Positional Systems

In modern positional numeral systems, the value of a symbol is determined by its place or position within the representation. For example, in the decimal system, the digit "2" represents different values depending on whether it appears in the tens or hundreds place. This efficient structure, which includes the Hindu-Arabic numerals, allows for complex arithmetic and is the foundation for other systems like binary and hexadecimal.12

Non-Positional Systems

Many ancient civilizations, such as the Egyptians, Greeks, and Romans, utilized non-positional systems. These often relied on:1
* Simple Grouping: Symbols were repeated to represent quantities, sometimes with special characters for powers of 10.3
* Additive and Subtractive Logic: In Roman numerals, symbols are added when placed after one of equal or greater value (e.g., VI = 6) and subtracted when placed before a larger value (e.g., IV = 4).4

While these systems were historically significant, their lack of positional value often complicated mathematical calculations compared to modern systems.1