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Numeral System
A NUMERAL SYSTEM (or SYSTEM OF NUMERATION) 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. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for _three_, the decimal symbol for _eleven_, or a symbol for other numbers in different bases . The number the numeral represents is called its value. Ideally, a numeral system will: * Represent a useful set of numbers (e.g. all integers , or rational numbers ) * Give every number represented a unique representation (or at least a standard representation) * Reflect the algebraic and arithmetic structure of the numbers.For example, the usual decimal representation of whole numbers gives every nonzero whole number a unique representation as a finite sequence of digits , beginning by a non-zero digit. However, when decimal representation is used for the rational or real numbers, such numbers in general have an infinite number of representations, for example 2.31 can also be written as 2.310, 2.3100000, 2.309999999..., etc., all of which have the same meaning except for some scientific and other contexts where greater precision is implied by a larger number of figures shown
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Number System
A NUMBER is a mathematical object used to count , measure , and label . The original examples are the natural numbers 1 , 2 , 3 , 4 and so forth. A notational symbol that represents a number is called a numeral . In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers ), for ordering (as with serial numbers ), and for codes (as with ISBNs ). In common usage, number may refer to a symbol, a word , or a mathematical abstraction . In mathematics , the notion of number has been extended over the centuries to include 0 , negative numbers , rational numbers such as 1/2 and −2/3, real numbers such as √2 and π , and complex numbers , which extend the real numbers by adding a square root of −1 . Calculations with numbers are done with arithmetical operations , the most familiar being addition , subtraction , multiplication , division , and exponentiation . Their study or usage is called arithmetic . The same term may also refer to number theory , the study of the properties of numbers. Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the number 13 is regarded as unlucky, and "a million " may signify "a lot." Though it is now regarded as pseudoscience , numerology , the belief in a mystical significance of numbers, permeated ancient and medieval thought
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Numeral (linguistics)
In linguistics , a NUMERAL is a member of a word class (or sometimes even a part of speech ) designating numbers , such as the English word 'two' and the compound 'seventy-seven'. Numerals function most typically as an adjective or a pronoun and express numbers and relations to numbers for example: quantity, sequence, frequency, or fraction. CONTENTS * 1 Identifying numerals * 2 Basis of counting system * 2.1 No base * 2.2 4: quaternary * 2.3 5: quinary * 2.4 6: senary * 2.5 8: octal * 2.6 10: decimal * 2.7 12: duodecimal * 2.8 20: vigesimal * 2.9 24: quadrovigesimal * 2.10 32: duotrigesimal * 2.11 60: sexagesimal * 2.12 80: octogesimal * 3 Larger numerals * 4 See also * 4.1 Numerals in various languages * 4.2 Related topics * 5 Notes * 6 Further reading IDENTIFYING NUMERALS "Collective numeral" redirects here. It is not to be confused with Collective number or Collective noun . Numerals may be attributive , as in TWO dogs, or pronominal , as in I saw TWO (of them). Many words of different parts of speech indicate number or quantity. Quantifiers do not enumerate, or designate a specific number, but give another, often less specific, indication of amount. Examples are words such as every, most, least, some, etc. Some times a quantifier can have a definite amount. Examples are words such as five, ten, fifty, one hundred, etc
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Hindu–arabic Numeral System
The HINDU–ARABIC NUMERAL SYSTEM (also called the ARABIC NUMERAL SYSTEM or HINDU NUMERAL SYSTEM) a positional decimal numeral system , is the most common system for the symbolic representation of numbers in the world. It was invented between the 1st and 4th centuries by Indian mathematicians . The system was adopted in Arabic
Arabic
mathematics by the 9th century. Influential were the books of Muḥammad ibn Mūsā al-Khwārizmī (_On the Calculation with Hindu
Hindu
Numerals_, c.825) and Al-Kindi (_On the Use of the Hindu
Hindu
Numerals_, c.830). The system later spread to medieval Europe
Europe
by the High Middle Ages . The system is based upon ten (originally nine) different glyphs . The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Brahmi numerals and have split into various typographical variants since the Middle Ages
Middle Ages
. These symbol sets can be divided into three main families: Arabic numerals used in the Greater Maghreb and in Europe
Europe
, Eastern Arabic numerals (also called "Indic numerals") used in the Middle East
Middle East
, and the Indian numerals used in the Indian subcontinent . This numerical system is still used worldwide today
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Arabic Numerals
ARABIC NUMERALS, also called HINDU–ARABIC NUMERALS are the ten digits : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system , the most common system for the symbolic representation of numbers in the world today. In this numeral system , a sequence of digits such as "975" is read as a single number, using the position of the digit in the sequence to interpret its value. The symbol for zero is the key to the effectiveness of the system, which was developed by ancient mathematicians in the Indian subcontinent around AD 500. The system was adopted by Arabic
Arabic
mathematicians in Baghdad
Baghdad
and passed on to the Arabs farther west. There is some evidence to suggest that the numerals in their current form developed from Arabic
Arabic
letters in the Maghreb
Maghreb
, the western region of the Arab world . The current form of the numerals developed in North Africa, distinct in form from the Indian and Eastern Arabic numerals . It was in the North African city of Bejaia
Bejaia
that the Italian scholar Fibonacci first encountered the numerals; his work was crucial in making them known throughout Europe and then further to the Europeans who spread it worldwide. The use of Arabic
Arabic
numerals spread around the world through European trade, books and colonialism
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Eastern Arabic Numerals
The EASTERN ARABIC NUMERALS (also called ARABIC–INDIC NUMERALS and ARABIC EASTERN NUMERALS) are the symbols used to represent the Hindu–Arabic numeral system , in conjunction with the Arabic alphabet in the countries of the Mashriq
Mashriq
(the east of the Arab world ), the Arabian Peninsula , and its variant in other countries that use the Perso-Arabic script in Asia
Asia
. CONTENTS * 1 Other names * 2 Numerals * 3 Usage * 4 Contemporary use * 5 References OTHER NAMESThese numbers are known as أرقام هندية ("Indian numbers") in Arabic. They are sometimes also called "Indic numerals" in English. However, that is sometimes discouraged as it can lead to confusion with Indian numerals , used in Brahmic scripts
Brahmic scripts
of India
India
. NUMERALS See also: Modern Arabic mathematical notation Each numeral in the Persian variant has a different Unicode point even if it looks identical to the Eastern Arabic
Arabic
numeral counterpart. However the variants used with Urdu
Urdu
, Sindhi , and other South Asian languages are not encoded separately from the Persian variants. See U+0660 through U+0669 and U+06F0 through U+06F9
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Bengali Numerals
BENGALI NUMERALS (সংখ্যা _shôngkhæ_), are the numeral system used in Bengali , Sylheti , Assamese , Bishnupriya Manipuri and Meithei languages. The Bengali numerals have more dominant usage in the Bengali and Assamese languages, unlike the dominant usage of Hindu numerals in most of the other world languages
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Gurmukhi Numerals
GURUMUKHI NUMERALS are the numeral system used in the Gurmukhi script for the Punjabi language in India . It is a variety of the many Indian numerals and are part of Hindu numeral system . In the Shahmukhi alphabet used for Punjabi in Pakistan, the Eastern Arabic-Indic numerals are used, similar to Persian and Urdu . BASE NUMBERSThere are various numberal systems of the Hindu numeral system in India. Below is a list of Gurumukhi numerals in their modern form with their Hindu-Arabic and Devanagari equivalents as well as their respective Punjabi and Hindi translations and transliterations
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Indian Numerals
INDIAN NUMERALS are the symbols representing numbers in India. These numerals are generally used in the context of the decimal Hindu–Arabic numeral system , and are distinct from, though related by descent to Arabic numerals . CONTENTS * 1 Devanagari numerals and their Hindi and Sanskrit names * 2 Other North Indic scripts * 3 South Indic scripts * 4 History * 5 See also * 6 References DEVANAGARI NUMERALS AND THEIR HINDI AND SANSKRIT NAMESBelow is a list of the Indian numerals in their modern Devanagari form, the corresponding Hindu-Arabic (European) equivalents, their Hindi and Sanskrit pronunciation, and translations in some languages
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Sinhala Numerals
Sinhalese belongs to the Indo-European language family with its roots deeply associated with Indo-Aryan sub family to which the languages such as Persian and Hindi belong. Although it is not very clear whether people in Sri Lanka
Sri Lanka
spoke a dialect of Prakrit at the time of arrival of Buddhism in Sri Lanka, there is enough evidence that Sinhala evolved from mixing of Sanskrit, Magadi (the language which was spoken in Magada Province of India where Lord Buddha was born) and local language which was spoken by people of Sri Lanka
Sri Lanka
prior to the arrival of Vijaya in Sri Lanka, the founder of Sinhala Kingdom. It is also surmised that Sinhala had evolved from an ancient variant of Apabramsa (middle Indic) which is known as ‘Elu’ . When tracing history of Elu, it was preceded by Hela or Pali
Pali
Sihala. Sinhala though has close relationships with Indo Aryan languages which are spoken primarily in the north, north eastern and central India, was very much influenced by Dravidian language families of Hindi.Though Sinhala is related closely to Indic languages, it also has its own unique characteristics: Sinhala has symbols for two vowels which are not found in any other Indic languages in India: ‘æ’ (ඇ) and ‘æ:’ (ඈ). The Sinhala script had evolved from Southern Brahmi script from which almost all the Southern Indic Scripts such as Telugu and Oriya had evolved
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Tamil Numerals
TAMIL NUMERALS (Tamil : தமிழ் எண்கள், இலக்கங்கள்), refers to the numeral system of the Tamil language
Tamil language
used officially in Tamil Nadu
Tamil Nadu
and Singapore
Singapore
, as well as by the other Tamil-speaking populations around the world including Mauritius
Mauritius
, Sri Lanka
Sri Lanka
, Malaysia
Malaysia
, Réunion
Réunion
, and South Africa
South Africa
, and other emigrant communities around the world
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Balinese Numerals
The Balinese language has an elaborate decimal numeral system. BASIC NUMERALSThe numerals 1–10 have basic, combining, and independent forms, many of which are formed through reduplication . The combining forms are used to form higher numbers. In some cases there is more than one word for a numeral, reflecting the Balinese register system; _halus_ (high-register) forms are listed in italics. Final orthographic _-a_ is a schwa . NUMERAL BASIC COMBINING INDEPENDENT 1 besik a-, sa-* abesik, aukud _(a)siki_ 2 dua duang- dadua _kalih_ _kalih-_ _kakalih_ 3 telu telung- tetelu _tiga_ _tigang-_ _tetiga_ 4 (em)pat petang- pa(t)pat 5 lima limang- lelima 6 (e)nem nem- ne(m)nem 7 pitu pitung- pepitu 8 (a)kutus kutus-, ulung- akutus 9 (a)sia sia-, sangang- Asia 10 (a)dasa dasa- adasa* A less productive combining form of _a-_ 1 is _sa-_, as can be seen in many of the numbers below. It, _ulung-_, and _sangang-_ are from Javanese . _Dasa_ 10 is from Sankrit _désa_. TEENS, TWEENS, AND TENSLike English, Balinese has compound forms for the teens and tens; however, it also has a series of compound 'tweens', 21–29. The teens are based on a root _*-welas_, the tweens on _-likur_, and the tens are formed by the combining forms above. Hyphens are not used in the orthography, but have been added to the table below to clarify their derivation
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Burmese Numerals
BURMESE NUMERALS (Burmese : မြန်မာဂဏန်း, ) are a set of numerals traditionally used in the Burmese language , although the Arabic numerals are also used. Burmese numerals follow the Hindu-Arabic numeral system commonly used in the rest of the world. CONTENTS* 1 Main numbers * 1.1 Zero to nine * 1.2 Ten to a million * 1.2.1 Round number rule * 1.3 Ordinal numbers * 1.4 Decimal and fractional numbers * 1.5 Alternate numbers * 2 References * 3 See also * 4 External links MAIN NUMBERS Burmese numerals in various script styles ZERO TO NINE NUMBER BURMESE NUMERAL Written ( MLCTS ) IPA 0 ၀ သုည1 _(su.nya.)_ IPA: 1 ၁ တစ် _(tac)_ IPA: 2 ၂ နှစ် _(hnac)_ IPA: 3 ၃ သုံး _(sum:)_ IPA: 4 ၄ လေး _(le:)_ IPA: 5 ၅ ငါး _(nga:)_ IPA: 6 ၆ ခြောက် _(hkrauk)_ IPA: 7 ၇ ခုနစ် _(hku. nac)_ IPA: 2 8 ၈ ရှစ် _(hrac)_ IPA: 9 ၉ ကိုး _(kui:)_ IPA: 10 ၁၀ ဆယ် _(ta. hcai)_ IPA: 1 Burmese for _zero _ comes from Sanskrit śūnya. 2 Can be abbreviated to IPA: in list contexts, such as telephone numbers. Spoken Burmese has innate pronunciation rules that govern numbers when they are combined with another word, be it a numerical place (e.g
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Dzongkha Numerals
Dzongkha , the national language of Bhutan
Bhutan
, has two numeral systems, one vigesimal (base 20), and a modern decimal system. The vigesimal system remains in robust use. Ten is an _auxiliary base_: the teens are formed with ten and the numerals 1–9. VIGESIMAL 1 ciː 11 cu-ci 2 ˈɲiː 12 cu-ɲi 3 sum 13 cu-sum 4 ʑi 14 cu-ʑi 5 ˈŋa 15 ce-ŋa 6 ɖʱuː 16 cu-ɖu 7 dyn 17 cup-dỹ 8 ɡeː 18 cop-ɡe 9 ɡuː 19 cy-ɡu 10 cu-tʰãm* 20 kʰe ciː*When it appears on its own, 'ten' is usually said _cu-tʰãm_ 'a full ten'. In combinations it is simply _cu_. Factors of 20 are formed from _kʰe_. Intermediate factors of ten are formed with _pɟʱe-da_ 'half to': 30 kʰe pɟʱe-da ˈɲiː (a half to two score) 40 kʰe ˈɲiː (two score) 50 kʰe pɟʱe-da sum (a half to three score) 100 kʰe ˈŋa (five score) 200 kʰe cutʰãm (ten score) 300 kʰe ceŋa (fifteen score)400 (20²) _ɲiɕu_ is the next unit: _ɲiɕu ciː_ 400, _ɲiɕu ɲi_ 800, etc. Higher powers are 8000 (20³) _kʰecʰe_ ('a ɡreat score') and _jãːcʰe_ 160,000 (20⁴). DECIMALThe decimal system is the same up to 19. Then decades, however, are formed as _unit–ten_, as in Chinese, and the hundreds similarly. 20 is reported to be _ɲiɕu_, the vigesimal numeral 400; this may be lexical interference for the expected *ɲi-cu
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Gujarati Numerals
GUJARATI NUMERALS is the numeral system of the Gujarati script of South Asia , which is a derivative of Devanagari numerals . It is the official numeral system of Gujarat, India . It is also officially recognized in India and as a minor script in Pakistan . BASE NUMBERSThe following table shows Gujarati numbers and the Gujarati word for each of them in various scripts. GUJARATI NUMERAL HINDU-ARABIC NUMERAL DEVANAGARI NUMERAL GUJARATI WORD LATIN DEVANAGARI ૦ 0 ० શૂન્ય shūnya शून्य ૧ 1 १ એક ēk एक ૨ 2 २ બે bē बे ૩ 3 ३ ત્રણ traṇ त्रण ૪ 4 ४ ચાર chār चार ૫ 5 ५ પાંચ pāṅch पांच ૬ 6 ६ છ chcha छ ૭ 7 ७ સાત sāt सात ૮ 8 ८ આઠ āṭh आठ ૯ 9 ९ નવ nav नवSEE ALSO * Gujarati script * Gurmukhi numerals * Devanagari alphabet REFERENCES * ^ "ScriptSource - Gujarati". Retrieved 2017-02-13. * ^ Benedikter, Thomas (2009). _Language Policy and Linguistic Minorities in India: An Appraisal of the Linguistic Rights of Minorities in India_. LIT Verlag Münster. p. 89. ISBN 978-3-643-10231-7
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Javanese Numerals
The Javanese language has a DECIMAL NUMERAL SYSTEM with distinct words for the 'tweens' from 21 to 29, called _likuran_. The basic numerals 1–10 have independent and combining forms, the latter derived via a suffix _-ng_. The combining forms are used to form the tens, hundreds, thousands, and millions. The numerals 1–5 and 10 have distinct high-register (_halus_, or in Javanese _krama_) and low register (_ngoko_) forms. The _halus_ forms are listed below in italics. (_Dasa_ 10 is derived from Sanskrit _désa_.) Like English, Javanese has compound forms for the teens; however, it also has a series of compound 'tweens', 21–29. The teens are based on a root _-(wə)las_, the tweens on _-likur_, and the tens are formed by the combining forms. Hyphens are not used in the orthography, but have been added to the table below to clarify their derivation. Final orthographic _-a_ tends to in many dialects, as does any preceding _a_ (as in _sanga_ 9)
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