The ten Arabic numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the most commonly used symbols for writing numbers. The term often also implies a positional notation using the numerals, as well as the use of a decimal base, in particular when contrasted with other systems such as Roman numerals. However, the symbols are also used to write numbers in other bases such as octal, as well as for writing non-numerical information such as trademarks or license plate identifiers.
The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any non-negative integer using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents.
0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic.
A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping.
A numerical digit or numeral is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.
Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus.
Positional notation usually denotes the extension to any base of the Hindu–Arabic numeral system. More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred. In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string.
Khmer numerals are the numerals used in the Khmer language. They have been in use since at least the early 7th century, with the earliest known use being on a stele dated to AD 604 found in Prasat Bayang, near Angkor Borei, Cambodia.
Brahmi numerals are a numeral system attested in the Indian subcontinent from the 3rd century BCE. It is the direct graphic ancestor of the modern Hindu–Arabic numeral system. However, the Brahmi numeral system was conceptually distinct from these later systems, as it was a non-positional decimal system, and did not include zero. Later additions to the system included separate symbols for each multiple of 10. There were also symbols for 100 and 1000, which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc. In computers, these ligatures are written with the Brahmi Number Joiner at U+1107F.
The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205".
The Hindu–Arabic numeral system is a positional base ten numeral system for representing integers; its extension to non-integers is the decimal numeral system, which is presently the most common numeral system.
The Eastern Arabic numerals, also called Indo-Arabic numerals, are the symbols used to represent numerical digits in conjunction with the Arabic alphabet in the countries of the Mashriq, the Arabian Peninsula, and its variant in other countries that use the Persian numerals on the Iranian plateau and in Asia.
A numeral is a character that denotes a number. The decimal number digits 0–9 are used widely in various writing systems throughout the world, however the graphemes representing the decimal digits differ widely. Therefore Unicode includes 22 different sets of graphemes for the decimal digits, and also various decimal points, thousands separators, negative signs, etc. Unicode also includes several non-decimal numerals such as Aegean numerals, Roman numerals, counting rod numerals, Mayan numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Western Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, such as ² or ②, and composite characters such as ½.
Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education. Its form is mostly derived from Western notation, but has some notable features that set it apart from its Western counterpart. The most remarkable of those features is the fact that it is written from right to left following the normal direction of the Arabic script. Other differences include the replacement of the Greek and Latin alphabet letters for symbols with Arabic letters and the use of Arabic names for functions and relations.
A timeline of numerals and arithmetic.
The Georgian numerals are the system of number names used in Georgian, a language spoken in the country of Georgia. The Georgian numerals from 30 to 99 are constructed using a base-20 system, similar to the scheme used in Basque, French for numbers 80 through 99, or the notion of the score in English.
An alphabetic numeral system is a type of numeral system. Developed in classical antiquity, it flourished during the early Middle Ages. In alphabetic numeral systems, numbers are written using the characters of an alphabet, syllabary, or another writing system. Unlike acrophonic numeral systems, where a numeral is represented by the first letter of the lexical name of the numeral, alphabetic numeral systems can arbitrarily assign letters to numerical values. Some systems, including the Arabic, Georgian and Hebrew systems, use an already established alphabetical order. Alphabetic numeral systems originated with Greek numerals around 600 BC and became largely extinct by the 16th century. After the development of positional numeral systems like Hindu–Arabic numerals, the use of alphabetic numeral systems dwindled to predominantly ordered lists, pagination, religious functions, and divinatory magic.
