numeracij

Numeracij, or numeration, is the system and practice of representing, naming, and counting numbers. It encompasses numeral systems, the words for numbers, and the rules for performing mathematical operations. Numeration provides the means to record quantities, order, and measurements across cultures and fields.

Historically, many forms of numeration have existed. Tally marks and counting boards were early methods for recording quantities. The ancient Egyptians and Babylonians used distinct numeral styles, with Babylonian math employing a sexagesimal base. The Hindu–Arabic numeral system, developed in India and transmitted through the Persian and Arabic scholarly world to Europe, introduced zero and a place-value decimal notation, which underpins most modern counting.

The most widely used system today is base-10 decimal, using digits 0–9 with place value. Other bases are common in specialized contexts, such as binary (base-2) in computing, octal (base-8), and hexadecimal (base-16). Non-positional systems exist too, such as Roman numerals, which express numbers without place value, and various character-based numerals in East Asian scripts. In language, numeration distinguishes cardinal numbers (one, two, three) from ordinal numbers (first, second, third).

In modern practice, numeration extends to computing and digital data, where binary and hexadecimal representations support programming and hardware design. Unicode and other text standards enable the representation of digits and numerals across many scripts, supporting multilingual numeration. Numeration thus bridges arithmetic, language, culture, and technology.