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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
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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
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Attic Numerals
ATTIC NUMERALS were used by the ancient Greeks , possibly from the 7th century BC. They were also known as HERODIANIC NUMERALS because they were first described in a 2nd-century manuscript by Herodian . They are also known as ACROPHONIC NUMERALS because the symbols derive from the first letters of the words that the symbols represent: five, ten, hundred, thousand and ten thousand. See Greek numerals
Greek numerals
and acrophony . DECIMAL SYMBOL GREEK NUMERAL IPA 1 Ι – – 5 Π πέντε 10 Δ δέκα 100 Η ἑκατόν 1000 Χ χίλιοι / χιλιάς 10000 Μ μύριονThe use of Η for 100 reflects the early date of this numbering system: Η (Eta ) in the early Attic alphabet represented the sound /h/. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked
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Mongolian Numerals
MONGOLIAN NUMERALS are numerals used mostly in conjunction with Mongolian script
Mongolian script
. They are still used on Mongolian tögrög banknotes. They are related to Tibetan numerals . COMPARISON TABLE HINDU-ARABIC NUMERALS MONGOLIAN NUMERALS TIBETAN NUMERALS 0 ᠐ ༠ 1 ᠑ ༡ 2 ᠒ ༢ 3 ᠓ ༣ 4 ᠔ ༤ 5 ᠕ ༥ 6 ᠖ ༦ 7 ᠗ ༧ 8 ᠘ ༨ 9 ᠙ ༩ This Mongolia
Mongolia
-related article is a stub . You can help by expanding it
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Javanese Numerals
The Javanese language
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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Āryabhaṭa Numeration
The ĀRYABHAṭA NUMERATION is a system of numerals based on Sanskrit phonemes . It was introduced in the early 6th century in India by Āryabhaṭa , in the first chapter titled Gītika Padam of his Aryabhatiya . It attributes a numerical value to each syllable of the form consonant+vowel possible in Sanskrit phonology , from ka = 1 up to hau = 1018 . CONTENTS * 1 History * 2 Example * 3 Numeral table * 4 See also * 5 References HISTORYThe basis of this number system is mentioned in the second stanza of the first chapter of Aryabhatiya . The Varga (Group/Class) letters ka to ma are to be placed in the varga (square) places (1st, 100th, 10000th, etc.) and Avarga letters like ya, ra, la .. have to be placed in Avarga places (10th, 1000th, 100000th, etc.). The Varga letters kak to ma have value from 1, 2, 3 .. up to 25 and Avarga letters ya to ha have value 30, 40, 50.. up to 100
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Hokkien Numerals
The Hokkien
Hokkien
language has two regularly used sets of numerals , a colloquial or native Hokkien
Hokkien
system and literary system. Literary and colloquial systems are not totally mutually independent; they are sometimes mixed used
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Japanese Numerals
The system of JAPANESE NUMERALS is the system of number names used in the Japanese language
Japanese language
. The Japanese numerals
Japanese numerals
in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000. Two sets of pronunciations for the numerals exist in Japanese: one is based on Sino-Japanese (on'yomi) readings of the Chinese characters
Chinese characters
and the other is based on the Japanese yamato kotoba (native words, kun\'yomi readings)
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Counting Rods
COUNTING RODS (traditional Chinese : 籌; simplified Chinese : 筹; pinyin : chóu; Japanese : 算木; rōmaji : sangi) are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China
China
, Japan
Japan
, Korea
Korea
, and Vietnam
Vietnam
. They are placed either horizontally or vertically to represent any integer or rational number . The written forms based on them are called ROD NUMERALS
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Vietnamese Numerals
Historically Vietnamese has two sets of numbers: one is etymologically native Vietnamese; the other uses Sino-Vietnamese vocabulary. In the modern language the native Vietnamese vocabulary is used for both everyday counting and mathematical purposes. The Sino-Vietnamese vocabulary is used only in fixed expressions or in Sino-Vietnamese words. This is somewhat analogous to the way in which Latin and Greek numerals
Greek numerals
are used in modern English (e.g., the bi- in bicycle). Sino-Vietnamese words are also used for units of ten thousand or above, where native vocabulary was lacking. CONTENTS * 1 Concept * 2 Basic figures * 3 Other figures * 4 Ordinal numbers * 5 Footnotes * 6 See also CONCEPTAmong the languages of the Chinese cultural sphere , Japanese and Korean both use two numerical systems, one native and one Chinese-based
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Korean Numerals
The Korean language
Korean language
has two regularly used sets of numerals , a native Korean system and Sino-Korean system. CONTENTS * 1 Construction * 2 Numerals (Cardinal) * 3 Pronunciation * 4 Constant suffixes used in Sino-Korean ordinal numerals * 5 Substitution for disambiguation * 6 Notes * 7 References * 8 See also CONSTRUCTIONFor both native and Sino- KOREAN NUMERALS, the teens (11 through 19) are represented by a combination of tens and the ones places. For instance, 15 would be sib-o (십오; 十五), but not usually il-sib-o in the Sino-Korean system, and yeol-daseot (열다섯) in native Korean. Twenty through ninety are likewise represented in this place-holding manner in the Sino-Korean system, while Native Korean has its own unique set of words, as can be seen in the chart below. The grouping of large numbers in Korean follow the Chinese tradition of myriads (10000) rather than thousands (1000)
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Burmese Numerals
BURMESE NUMERALS (Burmese : မြန်မာဂဏန်း, ) are a set of numerals traditionally used in the Burmese language
Burmese language
, although the Arabic numerals
Arabic numerals
are also used. Burmese numerals
Burmese numerals
follow the Hindu-Arabic numeral system
Hindu-Arabic numeral system
commonly used in the rest of the world
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Inuit Numerals
Inuit , like other Eskimo languages (and Celtic and Mayan languages as well), uses a vigesimal counting system. Inuit counting has sub-bases at 5, 10, and 15. Arabic numerals
Arabic numerals
, consisting of 10 distinct digits (0-9) are not adequate to represent a base-20 system. Students from Kaktovik, Alaska , came up with the KAKTOVIK INUPIAQ NUMERALS, which has since gained wide use among Alaskan Iñupiaq , and is slowly gaining ground in other countries where dialects of the Inuit language are spoken. The numeral system has helped to revive counting in Inuit, which had been falling into disuse among Inuit speakers due to the prevalence of the base-10 system in schools. The picture below shows the numerals 1–19 and then 0. Twenty is written with a one and a zero, forty with a two and a zero, and four hundred with a one and two zeros
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Quipu
QUIPUS, also known as KHIPUS or TALKING KNOTS, were recording devices historically used in a number of cultures and particularly in the region of Andean South America
South America
. Similar systems were used by the ancient Chinese and native Hawaiians, though this article specifically deals with the most familiar Inca
Inca
system, and knotted string records are often generically referred to in English as quipus after the Inca
Inca
term. A quipu usually consisted of colored, spun, and plied thread or strings made from cotton or camelid fiber. For the Inca, the system aided in collecting data and keeping records, ranging from monitoring tax obligations, properly collecting census records, calendrical information, and military organization. The cords contained numeric and other values encoded by knots in a base ten positional system. A quipu could have only a few or up to 2,000 cords
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Binary Number
In mathematics and digital electronics , a BINARY NUMBER is a number expressed in the BINARY NUMERAL SYSTEM or BASE-2 NUMERAL SYSTEM which represents numeric values using two different symbols: typically 0 (zero) and 1 (one) . The base -2 system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitry using logic gates , the binary system is used internally by almost all modern computers and computer-based devices . Each digit is referred to as a bit
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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
Hindu–Arabic numeral system
, in conjunction with the Arabic alphabet in the countries of the Mashriq (the east of the Arab world ), the Arabian Peninsula
Arabian Peninsula
, and its variant in other countries that use the Perso-Arabic script
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
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