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In linguistics, a number name, or numeral, is a symbol or group of symbols, or a word in a natural language that represents a number. Linguistics is the scientific study of Language, encompassing a number of sub-fields A word is a unit of Language that carries meaning and consists of one or more Morphemes which are linked more or less tightly together and has a Phonetic In the Philosophy of language, a natural language (or ordinary language) is a Language that is spoken or written in phonemic-alphabetic or phonemically-related A number is an Abstract object, tokens of which are Symbols used in Counting and measuring. Numerals differ from numbers just as words differ from the things they refer to. The symbols "11", "eleven" and "XI" are different numerals, all representing the same number. This article attempts to explain the various systems of numerals.

Contents

History

See also: Natural number
The numbers one through ten in different numeral systems
Indian ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩ ١٠
Devanagari १ २ ३ ४ ५ ६ ७ ८ ९ १०
Hebrew א ב ג ד ה ו ז ח ט י
Arabic 1 2 3 4 5 6 7 8 9 10
Malayalam ൧ ൨ ൩ ൪ ൫ ൬ ൭ ൮ ൯ ൧൦
Chinese 一 二 三 四 五 六 七 八 九 十
Suzhou 〡 〢 〣 〤 〥 〦 〧 〨 〩 〡〇
Roman I II III IV V VI VII VIII IX X
Thai ๑ ๒ ๓ ๔ ๕ ๖ ๗ ๘ ๙ ๑๐

Counting aids, especially the use of body parts (counting on fingers), were certainly used in prehistoric times as today. In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an There are many variations. Besides counting 10 fingers, some cultures have counted knuckles, the space between fingers, and toes as well as fingers. The Oksapmin culture of New Guinea uses a system of 27 upper body locations to represent numbers.

To preserve numerical information, Tallies carved in wood, bone, and stone have been used since prehistoric times. Tally marks are an implementation of the Unary numeral system. Stone age cultures, including ancient American Indian groups, used tallies for gambling, personal services, and trade-goods. For indigenous peoples in the United States other than Hawaii and Alaska see also Native Americans in the United States.

A method of preserving numeric information in clay was invented by the Sumerians between 8000 and 3500 BC. Sumer ( Sumerian: sux-Latn [[Ki (earth ki]]-[[EN (cuneiform en]]-'''ĝir15''', Akkadian: Šumeru; possibly Biblical Shinar This was done with small clay tokens of various shapes that were strung like beads on a string. Beginning about 3500 BC clay tokens were gradually replaced by number signs impressed with a round stylus at different angles in clay tablets (originally containers for tokens) which were then baked. About 3100 BC written numbers were dissociated from the things being counted and became abstract numerals.

Between 2700 BC and 2000 BC in Sumer, the round stylus was gradually replaced by a reed stylus that was used to press wedge-shaped cuneiform signs in clay. These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs. In Computers Sign-value notation (sign-magnitude notation in computers is the use of the high-order bit (left end of a binary word to represent the numeric sign 0 for + and These systems gradually converged on a common sexagesimal number system; this was a place-value system consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. Sexagesimal ( base-sixty) is a Numeral system with sixty as the base. This sexagesimal number system was fully developed at the beginning of the Old Babylonia period (about 1950 BC) and became standard in Babylonia.

Sexagesimal numerals were a mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons. Sexagesimal ( base-sixty) is a Numeral system with sixty as the base. Mixed radix Numeral systems are Non-standard positional numeral systems in which the numerical base varies from position to position By 1950 BC this was a positional notation system. A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a Sexagesimal numerals came to be widely used in commerce, but were also used in astronomical and other calculations. This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterranean nation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Egyptians. Babylonian-style sexagesimal numeration is still used in modern societies to measure time (minutes per hour) and angles (degrees). For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called

In China, armies and provisions were counted using modular tallies of prime numbers. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 Unique numbers of troops and measures of rice appear as unique combinations of these tallies. A great convenience of modular arithmetic is that it is easy to multiply, though quite difficult to add. In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers This makes use of modular arithmetic for provisions especially attractive. Conventional tallies are quite difficult to multiply and divide. In modern times modular arithmetic is sometimes used in Digital signal processing. Digital signal processing ( DSP) is concerned with the representation of the signals by a sequence of numbers or symbols and the processing of these signals

Numeral systems by culture
Hindu-Arabic numerals
Indian
Eastern Arabic
Khmer		 Indian family
Brahmi
Thai
East Asian numerals
Chinese
Suzhou
Counting rods		 Japanese
Korean 
Alphabetic numerals
Abjad
Armenian
Cyrillic
Ge'ez		 Hebrew
Greek (Ionian)
Āryabhaṭa
 
Other systems
Attic
Babylonian
Egyptian
Etruscan		 Mayan
Roman
Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
1, 3, 9, 12, 20, 24, 30, 36, 60, more…
v • d • e

The oldest Greek system was the that of the Attic numerals, but in the 4th century BC they began to use a quasidecimal alphabetic system (see Greek numerals). A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner The Hindu-Arabic numeral system is a Positional Decimal Numeral system first documented in the ninth century The arabic numerals (often capitalized are the ten Digits (0 1 2 3 4 5 6 7 8 9 which—along with the system The Eastern Arabic numerals (also called Arabic-Indic numerals and Arabic Eastern Numerals) are the symbols used to represent the Hindu-Arabic numeral system Khmer numerals are the numerals used in the Khmer language of Cambodia. Most of the positional Base 10 Numeral systems in the world have originated from India, which first developed the concept of positional numerology The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens Thai numerals (เลขไทย are a set of numerals traditionally used in Thailand, although the Arabic numerals are more common Chinese numerals are characters for writing Numbers in Chinese. The Suzhou numerals or huama is a Numeral system used in China before the introduction of Arabic numerals. Counting rods ( Japanese: 算木 sangi are small bars typically 3-14 cm long used by mathematicians for calculation in China, Japan The Korean language has two regularly used sets of numerals a Sino-Korean system and a native Korean system The Abjad numerals are a decimal Numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values The system of Armenian numerals is a historic Numeral system created using the Majuscules (uppercase letters of the Armenian alphabet. Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. Ge'ez (gez ግዕዝ) also called Ethiopic, is an Abugida script that was originally developed to write Ge'ez, a Semitic language The system of Hebrew numerals is a quasi-decimal alphabetic Numeral system using the letters of the Hebrew alphabet. ʹ the numeral sign redirects here For the accent ´ see Acute accent. The Āryabhaṭa numeration is a system of numerals based on Sanskrit phonemes. Attic numerals were used by the ancient Greeks, possibly from the 7th century BC Babylonian numerals were written in cuneiform, using a wedge-tipped reed Stylus to make a mark on a soft Clay tablet which would be exposed The system of Ancient Egyptian numerals was a Numeral system used in ancient Egypt aka Kemet The Etruscan numerals were used by the ancient Etruscans The system was adapted from the Greek Attic numerals and formed the inspiration for the later Roman The Pre-Columbian Maya civilization used a Vigesimal ( base - twenty) Numeral system. Roman numerals are a Numeral system originating in ancient Rome, adapted from Etruscan numerals. Discovery In 1946 a deposit with more than 250 sickles corresponding to the period 1500-1250 BC was discovered in Frankleben (in the region of Merseburg - Querfurt This is a list of Numeral system topics (and "numeric representations" by Wikipedia page A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a In mathematical numeral systems, the base or radix is usually the number of unique digits, including zero that a positional Numeral The decimal ( base ten or occasionally denary) Numeral system has ten as its base. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. Quaternary is the base - Numeral system. It uses the digits 0 1 2 and 3 to represent any Real number. The octal Numeral system, or oct for short is the base -8 number system and uses the digits 0 to 7 In Mathematics and Computer science, hexadecimal (also base -, hexa, or hex) is a Numeral system with a Base 32 or duotrigesimal is a Numeral system with 32 as its base The base - system is a Numeral system with 64 as its base It is the largest power-of-two base that can be represented using single printable ASCII The unary numeral system is the bijective base - 1 Numeral system. Ternary or trinary is the base - Numeral system. Analogous to a " Bit " a ternary digit is known as a trit ( Nonary is a base - Numeral system, typically using the digits 0-8 but not the digit 9 The duodecimal system (also known as base -12 or dozenal) is a Numeral system using twelve as its base. The vigesimal or base - numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten The base - system is a Numeral system with 24 as its base There are 24 hours in a day so our time keeping system includes a base-24 component Base 30 or trigesimal is a positional numeral system using 30 as the Radix. Base 36 is a positional numeral system using 36 as the Radix. Sexagesimal ( base-sixty) is a Numeral system with sixty as the base. Attic numerals were used by the ancient Greeks, possibly from the 7th century BC The 4th century BC started the first day of 400 BC and ended the last day of 301 BC. ʹ the numeral sign redirects here For the accent ´ see Acute accent. Jews began using a similar system (Hebrew numerals), with the oldest examples known being coins from around 100 BC. The system of Hebrew numerals is a quasi-decimal alphabetic Numeral system using the letters of the Hebrew alphabet.

The Roman empire used tallies written on wax, papyrus and stone, and roughly followed the Greek custom of assigning letters to various numbers. The Roman numerals system remained in common use in Europe until positional notation came into common use in the 1500s. Roman numerals are a Numeral system originating in ancient Rome, adapted from Etruscan numerals. A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a

The Maya of Central America used a mixed base 18 and base 20 system, possibly inherited from the Olmec, including advanced features such as positional notation and a zero. The Pre-Columbian Maya civilization used a Vigesimal ( base - twenty) Numeral system. The Olmec were an ancient Pre-Columbian people living in the Tropical lowlands of south-central Mexico, in what are roughly the modern-day states They used this system to make advanced astronomical calculations, including highly accurate calculations of the length of the solar year and the orbit of Venus. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University

The Incan Empire ran a large command economy using quipu, tallies made by knotting colored fibers. Quipu or khipu (sometimes called talking knots) were recording devices used in the Inca Empire and its predecessor societies in the Andean Knowledge of the encodings of the knots and colors was suppressed by the Spanish conquistadors in the 16th century, and has not survived although simple quipu-like recording devices are still used in the Andean region. Spain () or the Kingdom of Spain (Reino de España is a country located mostly in southwestern Europe on the Iberian Peninsula. This article is about the Spanish explorer soldiers of the fifteenth and sixteenth centuriesfor other uses see Conquistador (disambiguation A Conquistador The Andes form the world's longest exposed Mountain range. They lie as a continuous chain of highland along the western coast of South America.

Some authorities believe that positional arithmetic began with the wide use of counting rods in China. Counting rods ( Japanese: 算木 sangi are small bars typically 3-14 cm long used by mathematicians for calculation in China, Japan The earliest written positional records seem to be rod calculus results in China around 400. Rod calculus or rod calculation is the method of mathematical computation with Counting rods in China from The Warring States to Ming dynasty before the Events By Place Western Roman Empire Italy is first invaded by Alaric (probable date In particular, zero was correctly described by Chinese mathematicians around 932. Events By Place Europe St Ursenstift is founded by the Burgundian Queen Bertha in Solothurn.

The modern positional Arabic numeral system was developed by mathematicians in India, and passed on to Muslim mathematicians, along with astronomical tables brought to Baghdad by an Indian ambassador around 773. The Hindu-Arabic numeral system is a Positional Decimal Numeral system first documented in the ninth century Indian mathematics &mdashwhich here is the mathematics that emerged in South Asia zero, Negative numbers, Arithmetic, and Algebra. Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous Events By Place Europe Charlemagne crosses the Alps and invades the kingdom of the Lombards.

From India, the thriving trade between Islamic sultans and Africa carried the concept to Cairo. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country Cairo () which means "the Vanquisher" or "the Triumphant" is the capital and largest city of Egypt. Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th century. The decimal ( base ten or occasionally denary) Numeral system has ten as its base. The 9th century is the period from 801 to 900 in accordance with the Julian calendar in the Christian / Common Era. The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's Liber Abaci of 1201. The arabic numerals (often capitalized are the ten Digits (0 1 2 3 4 5 6 7 8 9 which—along with the system Leonardo of Pisa (c 1170 – c 1250 also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or most commonly simply Fibonacci In Europe, the complete Indian system with the zero was derived from the Arabs in the 12th century.

The binary system (base 2), was propagated in the 17th century by Gottfried Leibniz. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. As a means of recording the passage of Time, the 17th Century was that Century which lasted from 1601 - 1700 in the Gregorian calendar Leibniz had developed the concept early in his career, and had revisited it when he reviewed a copy of the I ching from China. The I Ching ( Wade-Giles) or “Yì Jīng” ( Pinyin) also called “Classic of Changes” or “Book of Changes” is one of the oldest of the Binary numbers came into common use in the 20th century because of computer applications. The twentieth century of the Common Era began on

Counting base

Although a majority of traditional number systems are based on the decimal numeral system, there are many regional variations even within decimal, including:

Duodecimal numbers have only been used consistently in a few cases. Most of the positional Base 10 Numeral systems in the world have originated from India, which first developed the concept of positional numerology The duodecimal system (also known as base -12 or dozenal) is a Numeral system using twelve as its base. Among these, the Chepang language of Nepal, the Mahl language of Minicoy Island in India, and several languages of the Nigerian Middle Belt, such as Janji, Kahugu and the Nimbia dialect of Gwandara. Chepang is the commonly used name given to an indigenous ethnic group living in central and southern Nepal. Nepal (नेपाल) is a Landlocked country in South Asia. Mahal (މަހަލް or Mahl, also known locally as Maliku Bas, is an Indo-Aryan language spoken by the people of Minicoy Island ( Maliku Minicoy Island or Maliku is the only inhabited island of the Maliku Atoll and is located at. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country Nigeria, officially named the Federal Republic of Nigeria, is a federal Constitutional republic comprising thirty-six states and one Federal The Middle Belt is a human geographical term designating the region of central Nigeria populated largely by Minority ethnic groups and stretching across the country However, duodecimal subdivisions offer practical advantages over decimal because of the better divisibility of twelve (which is a highly composite number), and as such they have been used extensively in many other cultures as well; for example, in time divisions (twelve months in a year, the twelve-hour clock), in the imperial system of units (twelve inches to the foot, twelve Troy ounces to the Troy pound), or in the former British monetary system (twelve pence to the shilling). A highly composite number ( HCN) is a positive Integer with more Divisors than any smaller positive integer Imperial units or the Imperial system is a collection of units first defined in the British Weights and Measures Act of 1824 As a result, languages such as English eventually borrowed or evolved terms such dozen, gross and great gross, which allow for a rudimentary duodecimal nomenclature (e. Dozen is another word for the Number twelve. The dozen may be one of the earliest primitive groupings perhaps because there are approximately a dozen cycles of the A gross is equal to a Dozen dozen ie 12 × 12 = 144. It can be used in Duodecimal counting In mathematics It is the cube of 12, and as g. , saying "two gross and six dozen" instead of "three hundred and sixty"). Ancient Romans used decimal for integers, but switched to duodecimal for fractions, and correspondingly Latin developed a rich vocabulary for duodecimal-based fractions (see Roman numerals). Ancient Rome was a Civilization that grew out of a small agricultural community founded on the Italian Peninsula as early as the 10th century BC Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Roman numerals are a Numeral system originating in ancient Rome, adapted from Etruscan numerals. In fiction, J. R. R. Tolkien's Elvish languages used duodecimal along with decimal. Elvish languages are Constructed languages used typically by elves in a Fantasy setting

Vigesimal numbers were the standard among ancient Mesoamerican cultures, and are still in use in the modern indigenous languages of their present-day descendants, such as the Nahuatl and Mayan languages (see also Maya numerals). The vigesimal or base - numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten Mesoamerica or Meso-America (Mesoamérica is a Region extending approximately from central Mexico to Honduras and Nicaragua, defined Nahuatl ( is a group of related languages and dialects of the Aztecan or Nahuan branch of the Uto-Aztecan language family The Pre-Columbian Maya civilization used a Vigesimal ( base - twenty) Numeral system. Vigesimal terminology is also found to some extent in some European languages (Basque, Celtic languages, French, Danish, Georgian). Basque ( native name: euskara) is the Language spoken by the Basque people who inhabit the Pyrenees in North-Central Spain The Celtic languages are descended from Proto-Celtic, or "Common Celtic" a branch of the greater Indo-European Language family. French ( français,) is a Romance language spoken around the world by 118 million people as a native language and by about 180 to 260 million people Danish ( d̥ænsɡ̊ is one of the North Germanic languages (also called Scandinavian languages a sub-group of the Germanic branch of the Georgian (ka ქართული ენა kartuli ena) is the Official language of Georgia, a country in the Caucasus. English has a remnant of vigesimal numeration in the word score (famously used in the opening of the Gettysburg Address). "Twenty" redirects here For the village in England, see Twenty Lincolnshire. The Gettysburg Address is a speech by US President Abraham Lincoln and one of the most quoted speeches in United States history.

Quinary is found in Inuit languages. Quinary ( base -) is a Numeral system with five as the base This originates from the five Fingers on either Hand. The Inuit language is traditionally spoken across the North American Arctic and to some extent in the Subarctic in Labrador.

Octal is used in the Yuki language of California and in the Pamean languages of Mexico, because their speakers count using the spaces between their fingers rather than the fingers themselves. The octal Numeral system, or oct for short is the base -8 number system and uses the digits 0 to 7 The Yuki (also Yukian, Ukiah, Ukomno'm) language was a Yuki-Wappo language of California spoken by the Yuki Indians. California ( is a US state on the West Coast of the United States, along the Pacific Ocean. The United Mexican States ( or commonly Mexico (ˈmɛksɪkoʊ () is a federal constitutional Republic in North America. [1]

For very large (and very small) numbers, traditional systems have been superseded by the use of scientific notation and the system of SI prefixes. Scientific notation, also sometimes known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol to form a Decimal multiple or Traditional systems continue to be used in everyday life.

Systems of numerals

See also

References

  1. ^ Ascher, Marcia (1994), Ethnomathematics: A Multicultural View of Mathematical Ideas, Chapman & Hall, ISBN 0412989417 
The Hindu-Arabic numeral system is a Positional Decimal Numeral system first documented in the ninth century The system of Armenian numerals is a historic Numeral system created using the Majuscules (uppercase letters of the Armenian alphabet. Babylonian numerals were written in cuneiform, using a wedge-tipped reed Stylus to make a mark on a soft Clay tablet which would be exposed Chinese numerals are characters for writing Numbers in Chinese. The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French ʹ the numeral sign redirects here For the accent ´ see Acute accent. The system of Hebrew numerals is a quasi-decimal alphabetic Numeral system using the letters of the Hebrew alphabet. The Indian numbering system, used today in India, Pakistan, Bangladesh, Nepal and Myanmar (Burma is based on grouping by two The Korean language has two regularly used sets of numerals a Sino-Korean system and a native Korean system The Pre-Columbian Maya civilization used a Vigesimal ( base - twenty) Numeral system. Quipu or khipu (sometimes called talking knots) were recording devices used in the Inca Empire and its predecessor societies in the Andean Counting rods ( Japanese: 算木 sangi are small bars typically 3-14 cm long used by mathematicians for calculation in China, Japan Roman numerals are a Numeral system originating in ancient Rome, adapted from Etruscan numerals. An abacus, also called a counting frame, is a calculating tool used primarily by Asians for performing arithmetic processes Different Cultures used different traditional Numeral systems for naming large numbers. The following tables list the names and symbols for the numbers 0 through 10 in various Languages and scripts of the world This is a list of Numeral system topics (and "numeric representations" by Wikipedia page The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French Myriad is a classical Greek name for the Number 104 = 10000. In modern English the word refers to an unspecified large quantity Names of numbers larger than a quadrillion are almost never used for reasons discussed further below A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner
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