# Numeral

A number sign or a digit (derived from Arabic صفر, DMG ṣifr “zero, nothing”, which in turn translates Sanskrit śūnyā , “empty”) is a character to which a number , the numerical value , is assigned as a value and which is used in a number system to represent numbers . Such a representation consists of one or more number characters (such as a sequence of digits ) and, if necessary, further symbols such as prefixes and separators. The way a number is represented depends on the number system used. Numbers of the same origin form a number font (for example the Roman numerals ), comparable for example with letters of the same origin that form an alphabet font (for example the Roman alphabet font ).

The terms numeral and digit are often used synonymously . However, the concept of the number is etymologically closely related to the place value system. Because digit means - as already noted in the introduction - "nothing" or "zero", and numerals for zero were predominantly used in place value systems - which require them. The term number, on the other hand, stands for mathematical abstractions , which are to be distinguished from numerals.

## history

In different cultures there were and are different number fonts , with numbers, letters or symbols being used as numerals. The simplest number signs are bars, the number of which represents the desired number.

Today the so-called Arabic numerals (in different regional variations) are predominant. The Roman numeral is sometimes still found today as the year of construction on buildings, e.g. B. MDCCCLXXXIV for 1884, or as the year of publication in film credits, e.g. B. MMI for 2001.

## Use in number systems

Each number system only uses a certain amount of characters and uses them according to precisely defined rules. Strings that do not conform to these rules are not valid number symbols. One can differentiate between place value systems and addition systems.

The most common place value systems are the decimal system on the base 10 with 10 digits (0 to 9), the binary or dual system on the base 2 with 2 digits (e.g. 0 and 1) and the hexadecimal system on the base 16 with 16 digits (usually as 0,1,2,3,4,5,6,7,8,9, A, B, C, D, E, F). The time, measured in hours, minutes and seconds, is similar to a base 60 place value system and is called the sexagesimal system . Place value systems only use integer numerical values ​​that are smaller in amount than their base.

The most common addition system is, besides the unary system (“tally”), the Roman one . In addition systems, all positive rational numbers as well as zero can in principle appear as numerical values; mostly natural numbers are shown.

Numbers in addition systems symbolize the same number regardless of their position: In Roman spelling, the V always stands for five. In contrast, a number in a place value system stands for the product of digit value and place value : The "5" in the number 53 is worth ten times as much ("fifty") as in the number 35 ("five"). The place value is the power of the base that corresponds to the position of the digit in the digit sequence. For example, the “3” in “13” stands for three whole, in “0.354” on the other hand for three tenths, and in the hexadecimal notation “3B” for three times 16.

## Number representation

In different number systems, a number is usually represented by different sequences of digits. Thus, for example, the number ten is written as decimal “10”, binary as “1010”, hexadecimal as “A” and Roman as “X”.

Conversely, a sequence of digits in the different number systems in which it is defined usually symbolizes different numbers. For example, the sequence of digits “10” symbolizes the respective base in all place value systems (decimal 10, binary 2, hexadecimal 16, ...). In the Roman system it is not a valid number symbol.

Within a number system, each valid number symbol represents exactly one number. Conversely, a number but are represented by different sequences of digits such as, for example, the number seven decimal through "7", "007", "+7.0", "07.0000" or "+06, 9 ".