1.
Numeral system
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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. It can be seen as the context that allows the symbols 11 to be interpreted as the 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 Give every number represented a unique representation Reflect the algebraic and arithmetic structure of the numbers. For example, the decimal representation of whole numbers gives every nonzero whole number a unique representation as a finite sequence of digits. Etc. all of which have the same meaning except for some scientific, such systems are, however, not the topic of this article. The most commonly used system of numerals is the Hindu–Arabic numeral system, two Indian mathematicians are credited with developing it. Aryabhata of Kusumapura developed the notation in the 5th century. The numeral system and the concept, developed by the Hindus in India, slowly spread to other surrounding countries due to their commercial. The Arabs adopted and modified it, even today, the Arabs call the numerals which they use Rakam Al-Hind or the Hindu numeral system. The Arabs translated Hindu texts on numerology and spread them to the world due to their trade links with them. The Western world modified them and called them the Arabic numerals, hence the current western numeral system is the modified version of the Hindu numeral system developed in India. It also exhibits a great similarity to the Sanskrit–Devanagari notation, which is used in India. The simplest numeral system is the numeral system, in which every natural number is represented by a corresponding number of symbols. If the symbol / is chosen, for example, then the seven would be represented by ///////. Tally marks represent one such system still in common use, the unary system is only useful for small numbers, although it plays an important role in theoretical computer science. Elias gamma coding, which is used in data compression. The unary notation can be abbreviated by introducing different symbols for new values. The ancient Egyptian numeral system was of type, and the Roman numeral system was a modification of this idea
2.
Arabic numerals
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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, the system was adopted by Arab mathematicians in 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 letters in the Maghreb, the current form of the numerals developed in North Africa, distinct in form from the Indian and eastern Arabic numerals. The use of Arabic numerals spread around the world through European trade, books, the term Arabic numerals is ambiguous. It most commonly refers to the widely used in Europe. Arabic numerals is also the name for the entire family of related numerals of Arabic. It may also be intended to mean the numerals used by Arabs and it would be more appropriate to refer to the Arabic numeral system, where the value of a digit in a number depends on its position. The decimal Hindu–Arabic numeral system was developed in India by AD700, the development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmaguptas formulation of zero as a number in AD628. The system was revolutionary by including zero in positional notation, thereby limiting the number of digits to ten. It is considered an important milestone in the development of mathematics, one may distinguish between this positional system, which is identical throughout the family, and the precise glyphs used to write the numerals, which varied regionally. The glyphs most commonly used in conjunction with the Latin script since early modern times are 0123456789. The first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. Numerous Indian documents on copper plates exist, with the symbol for zero in them, dated back as far as the 6th century AD. Inscriptions in Indonesia and Cambodia dating to AD683 have also been found and their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. In the 10th century, Middle-Eastern mathematicians extended the decimal system to include fractions. The decimal point notation was introduced by Sind ibn Ali, who wrote the earliest treatise on Arabic numerals. Ghubar numerals themselves are probably of Roman origin, some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin. In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals, Algoritmi, the translators rendition of the authors name, gave rise to the word algorithm
3.
Eastern Arabic numerals
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These numbers are known as أرقام هندية 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 of India. Each numeral in the Persian variant has a different Unicode point even if it looks identical to the Eastern Arabic numeral counterpart, however the variants used with 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, written numerals are arranged with their lowest-value digit to the right, with higher value positions added to the left. That is identical to the arrangement used by Western texts using Hindu-Arabic numerals even though Arabic script is read from right to left. There is no conflict unless numerical layout is necessary, as is the case for arithmetic problems and lists of numbers, Eastern Arabic numerals remain strongly predominant vis-à-vis Western Arabic numerals in many countries to the East of the Arab world, particularly in Iran and Afghanistan. In Pakistan, Western Arabic numerals are more used as a considerable majority of the population is anglophone. Eastern numerals still continue to see use in Urdu publications and newspapers, in North Africa, only Western Arabic numerals are now commonly used. In medieval times, these used a slightly different set
4.
Indian numerals
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Indian numerals are the symbols representing numbers in India. These numerals are used in the context of the decimal Hindu–Arabic numeral system. Below is a list of the Indian numerals in their modern Devanagari form, the corresponding Hindu-Arabic equivalents, their Hindi and Sanskrit pronunciation, since Sanskrit is an Indo-European language, it is obvious that the words for numerals closely resemble those of Greek and Latin. The word Shunya for zero was translated into Arabic as صفر sifr, meaning nothing which became the zero in many European languages from Medieval Latin. The five Indian languages that have adapted the Devanagari script to their use also naturally employ the numeral symbols above, of course, for numerals in Tamil language see Tamil numerals. For numerals in Telugu language see Telugu numerals, Tamil and Malayalam scripts also have distinct forms for 10,100,1000 numbers, ௰, ௱, ௲and ൰, ൱, ൲ respectively in tamil and scripts. A decimal place system has been traced back to ca.500 in India, before that epoch, the Brahmi numeral system was in use, that system did not encompass the concept of the place-value of numbers. Instead, Brahmi numerals included additional symbols for the tens, as well as symbols for hundred. The Indian place-system numerals spread to neighboring Persia, where they were picked up by the conquering Arabs, in 662, Severus Sebokht - a Nestorian bishop living in Syria wrote, I will omit all discussion of the science of the Indians. Of their subtle discoveries in astronomy — discoveries that are more ingenious than those of the Greeks, I wish only to say that this computation is done by means of nine signs. But it is in Khmer numerals of modern Cambodia where the first extant material evidence of zero as a numerical figure, as it was from the Arabs that the Europeans learned this system, the Europeans called them Arabic numerals, the Arabs refer to their numerals as Indian numerals. In academic circles they are called the Hindu–Arabic or Indo–Arabic numerals, but what was the net achievement in the field of reckoning, the earliest art practiced by man. An inflexible numeration so crude as to progress well nigh impossible. Man used these devices for thousands of years without contributing an important idea to the system. Even when compared with the growth of ideas during the Dark Ages. When viewed in light, the achievements of the unknown Hindu. Sanskrit Siddham Numbers Karl Menninger, Number Words and Number Symbols - A Cultural History of Numbers ISBN 0-486-27096-3 David Eugene Smith and Louis Charles Karpinski, The Hindu-Arabic Numerals
5.
Sinhala numerals
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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. It is also surmised that Sinhala had evolved from an ancient variant of Apabramsa which is known as ‘Elu’, when tracing history of Elu, it was preceded by Hela or Pali Sihala. The Sinhala script had evolved from Southern Brahmi script from which almost all the Southern Indic Scripts such as Telugu, later Sinhala was influenced by Grantha writing of Southern India. Since 1250 AD, the Sinhala script had remained the same with few changes, although some scholars are of the view that the Brahmi Script arrived with the Buddhism, Mahavamsa speaks of written language even right after the arrival of Vijaya. Archeologists had found pottery fragments in Anuradhapura Sri Lanka with older Brahmi script inscriptions, the earliest Brahmi Script found in India had been dated to 6th Century BC in Tamil Nadu though most of Brahmi writing found in India had been attributed to emperor Ashoka in the 3rd century BC. Sinhala letters are round-shaped and are written left to right. The evolution of the script to the present shapes may have taken place due to writing on Ola leaves, unlike chiseling on a rock, writing on palm leaves has to be more round-shaped to avoid the stylus ripping the Palm leaf while writing on it. When drawing vertical or horizontal lines on Ola leaf, the leaves would have been ripped. Instead a stylistic stop which was known as ‘Kundaliya’ is used, period and commas were later introduced into Sinhala script after the introduction of paper due to the influence of Western languages. In modern Sinhala, Arabic numerals, which were introduced by Portuguese, Dutch and English, is used for writing numbers and it is accepted that Arabic numerals had evolved from Brahmi numerals. This article will touch upon Brahmi numerals, which were found in Sri Lanka. It had been found five different types of numerations were used in the Sinhala language at the time of the invasion of the Kandyan kingdom by the British. Out of the five types of numerations, two sets of numerations were in use in the century mainly for astrological calculations and to express traditional year. The five types or sets of numerals or numerations are listed below, according to Mr. Gunesekera, these numerals were used for ordinary calculations and to express simple numbers. These numerals had separate Symbols for 10,40,50,100,1000 and these numerals were also regarded as Lith Lakunu or ephemeris numbers by W. A. De Silva in his “Catalogue of Palm leaf manuscripts in the library of Colombo Museum”. This set of numerals was known as Sinhala illakkam or Sinhala archaic numerals, Arabic Figures are now universally used. For the benefit of the student, the old numerals are given in the plate opposite,11 clauses had been numbered in Arabic numerals in the English part of the agreement and in parallel Sinhala clauses were numbered in Sinhala archaic numerals. Numbers of lith illakkam look Sinhala letters and vowel modifiers, the number six is known as ‘akma’ in the Lith Illakkam
6.
Tamil numerals
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Traditionally Vattezhuttu characters were used, but now Arabic numerals have become commonplace. Old Tamil possesses a special character for zero and it is read as andru. But yet Modern Tamil renounces the use of its native character, Modern Tamil words for zero include சுழியம் or பூச்சியம். Tamil has a prefix for each number from 1 to 9. For instance, the word for fifty, ஐம்பது is a combination of ஐ, the prefix for nine changes with respect to the succeeding base 10. தொ+ the unvoiced consonant of the succeeding base 10 forms the prefix for nine, for instance,90 is தொ+ண், hence, தொண்ணூறு). These are typically void in the Tamil language except for some Hindu and Christian religious references, example அட்ட இலட்சுமிகள் in a Hindu context, unlike other Indian languages, Tamil has distinct digits for 10,100, and 1000. It also has characters for other number-based aspects of day-to-day life. − − − − − − − − − − − − There are two systems that can be used in the Tamil language, the Tamil system which is as follows. The following are the numbers of the Ancient Tamil Country. Sanskrit based multiples like lakhs are also followed just like other Indian languages and you can transcribe any fraction, by affixing -இல் after the denominator followed by the numerator. For instance, 1/41 can be said as நாற்பத்து ஒன்றில் ஒன்று, the suffixing of the -இல் requires you to change the last consonant of the number to its இ form. For example, மூன்று+இல் becomes மூன்றில், note the உ has been omitted, common fractions have names already allocated to them, hence, these names are often used rather than the above method. Other fractions are, Anu was considered as lowest fraction by ancient Tamils as size of smallest physical object, later, this term went to Sanskrit to refer directly atom. Decimal point is called புள்ளி in Tamil, for example,1.1 would be read as ஒன்று புள்ளி ஒன்று. Percentage is known as விழுக்காடு in Tamil or சதவீதம் and these words are simply added after a number to form percentages. For instance, four percent is நான்கு சதவீதம் or நான்கு விழுக்காடு, percentage symbol is also recognised and used. Ordinal numbers are formed by adding the suffix -ஆம் after the number, as always, when blending two words into one, an unvoiced form of the consonant as the one that the second starts with, is placed in between to blend
7.
Balinese numerals
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The Balinese language has an elaborate decimal numeral system. The numerals 1–10 have basic, combining, and independent forms, 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, final orthographic -a is a schwa. * A less productive combining form of a-1 is sa- and it, ulung-, and sangang- are from Javanese. Dasa 10 is from Sankrit désa, like 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, hyphens are not used in the orthography, but have been added to the table below to clarify their derivation. The high-register combining forms kalih-2 and tigang-3 are used with -likur, -dasa, and higher numerals, the teens are from Javanese, where the -olas forms are regular, apart from pele-kutus 18, which is suppletive. Sa-laé25, and se-ket 50 are also suppletive, and cognate with Javanese səlawé25, there are additional numerals pasasur ~ sasur 35 and se-timahan ~ se-timan 45, and a compound telung-benang for 75. The unit combining forms are combined with atus 100, atak 200, amas 400, tali 1000, laksa 10,000, keti 100,000, in addition, there is karobelah 150, lebak 175, and sepa for 1600. At least karobelah has a cognate in Javanese, ro-bəlah, where ro- is the form for two
8.
Burmese numerals
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Burmese numerals 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 used in the rest of the world. 1 Burmese for zero comes from Sanskrit śūnya.2 Can be abbreviated to IPA, in list contexts, spoken Burmese has innate pronunciation rules that govern numbers when they are combined with another word, be it a numerical place or a measure word. Other suffixes such as ထောင်, သောင်း, သိန်း, and သန်း all shift to, for six and eight, no pronunciation shift occurs. These pronunciation shifts are exclusively confined to spoken Burmese and are not spelt any differently,1 Shifts to voiced consonant following three, four, five, and nine. Ten to nineteen are almost always expressed without including တစ်, another pronunciation rule shifts numerical place name from the low tone to the creaky tone. Number places from 10 up to 107 has increment of 101, beyond those Number places, larger number places have increment of 107. 1014 up to 10140 has increment of 107, numbers in the hundreds place, shift from ရာ to ရာ့, except for numbers divisible by 100. Numbers in the place, shift from ထောင် to ထောင့်. Hence, a number like 301 is pronounced, while 300 is pronounced, the digits of a number are expressed in order of decreasing digits place. When a number is used as an adjective, the word order is. However, for numbers, the word order is flipped to. The exception to rule is the number 10, which follows the standard word order. Ordinal numbers, from first to tenth, are Burmese pronunciations of their Pali equivalents and they are prefixed to the noun. Beyond that, cardinal numbers can be raised to the ordinal by suffixing the particle မြောက် to the number in the order, number + measure word + မြောက်. Colloquially, decimal numbers are formed by saying ဒသမ where the separator is located. For example,10.1 is ဆယ် ဒသမ တစ်, half is expressed primarily by တစ်ဝက်, although ထက်ဝက်, အခွဲ and အခြမ်း are also used. Quarter is expressed with အစိတ် or တစ်စိတ်, other fractional numbers are verbally expressed as follows, denominator + ပုံ + numerator + ပုံ
9.
Dzongkha numerals
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Dzongkha, the national language of Bhutan, has two numeral systems, one vigesimal, 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. *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,400 ɲiɕu is the next unit, ɲiɕu ciː400, ɲiɕu ɲi 800, etc. Higher powers are 8000 kʰecʰe and jãːcʰe 160,000, the decimal system is the same as the vigesimal system up to 19. Then decades, however, are formed as unit–ten, as in Chinese,20 is reported to be ɲiɕu, the vigesimal numeral 400, this may be lexical interference for the expected *ɲi-cu. Mazaudon & Lacito,2002, Les principes de construction du nombre dans les langues tibeto-birmanes, in François, ed
10.
Gujarati numerals
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Gujarati numerals is the numeral system of the Gujarati script of South Asia, which is a derivative of Devanagari numerals. It is the numeral system of Gujarat, India. It is also recognized in India and as a minor script in Pakistan. The following table shows Gujarati numbers and the Gujarati word for each of them in various scripts, Gujarati script Gurmukhi numerals Devanagari alphabet
11.
Javanese numerals
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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 and low register forms, the halus forms are listed below in italics. Like English, Javanese has compound forms for the teens, however, it also has a series of compound tweens, the teens are based on a root -las, the tweens on -likur, and the tens are formed by the combining forms. Hyphens are not used in the orthography, but have added to the table below to clarify their derivation. Final orthographic -a tends to in many dialects, as does any preceding a, parallel to the tens are the hundreds, the thousands, and the millions, except that the compounds of five and six are formed with limang- and nem-. The names of the Old Javanese numerals were derived from their names in the Sanskrit language, balinese numerals, a related but yet more complex numeral system
12.
Khmer numerals
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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 AD604 found in Prasat Bayang, Cambodia, having been derived from the Hindu numerals, modern Khmer numerals also represent a decimal positional notation system. It is the script with the first extant material evidence of zero as a figure, dating its use back to the seventh century. However, Old Khmer, or Angkorian Khmer, also possessed separate symbols for the numbers 10,20 and this inconsistency with its decimal system suggests that spoken Angkorian Khmer used a vigesimal system. For example,6 is formed from 5 plus 1, with the exception of the number 0, which stems from Sanskrit, the etymology of the Khmer numbers from 1 to 5 is of proto-Mon–Khmer origin. For details of the various alternative romanization systems, see Romanization of Khmer, some authors may alternatively mark as the pronunciation for the word two, and either or for the word three. In neighbouring Thailand the number three is thought to bring good luck, however, in Cambodia, taking a picture with three people in it is considered bad luck, as it is believed that the person situated in the middle will die an early death. As mentioned above, the numbers from 6 to 9 may be constructed by adding any number between 1 and 4 to the base number 5, so that 7 is literally constructed as 5 plus 2. Beyond that, Khmer uses a base, so that 14 is constructed as 10 plus 4, rather than 2 times 5 plus 4. In constructions from 6 to 9 that use 5 as a base, /pram/ may alternatively be pronounced, giving and this is especially true in dialects which elide /r/, but not necessarily restricted to them, as the pattern also follows Khmers minor syllable pattern. The numbers from thirty to ninety in Khmer bear many resemblances to both the modern Thai and Cantonese numbers, informally, a speaker may choose to omit the final and the number is still understood. For example, it is possible to say instead of the full, Language Comparisons, Words in parenthesis indicate literary pronunciations, while words preceded with an asterisk mark are non-productive. The standard Khmer numbers starting from one hundred are as follows, Although មួយកោដិ is most commonly used to mean ten million, in some areas this is also colloquially used to refer to one billion. In order to avoid confusion, sometimes ដប់លាន is used to mean ten million, along with មួយរយលាន for one hundred million, different Cambodian dialects may also employ different base number constructions to form greater numbers above one thousand. As a result of prolonged literary influence from both the Sanskrit and Pali languages, Khmer may occasionally use borrowed words for counting. One reason for the decline of numbers is that a Khmer nationalism movement. The Khmer Rouge also attempted to cleanse the language by removing all words which were considered politically incorrect, Khmer ordinal numbers are formed by placing the word ទី in front of a cardinal number. This is similar to the use of ที่ thi in Thai and it is generally assumed that the Angkorian and pre-Angkorian numbers also represented a dual base system, with both base 5 and base 20 in use
13.
Lao alphabet
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Lao script, or Akson Lao, is the primary script used to write the Lao language and other minority languages in Laos. It was also used to write the Isan language, but was replaced by the Thai script and it has 27 consonants,7 consonantal ligatures,33 vowels, and 4 tone marks. Akson Lao is a system to the Thai script, with which it shares many similarities. However, Lao has fewer characters and is formed in a curvilinear fashion than Thai. Lao is traditionally written from left to right, Lao is considered an abugida, in which certain implied vowels are unwritten. However, due to spelling reforms by the communist Lao Peoples Revolutionary Party, despite this, most Lao outside of Laos, and many inside Laos, continue to write according to former spelling standards, so vernacular Lao functions as a pure abugida. For example, the old spelling of ສເລີມ to hold a ceremony, vowels can be written above, below, in front of, or behind consonants, with some vowel combinations written before, over and after. Spaces for separating words and punctuation were traditionally not used, but a space is used, the letters have no majuscule or minuscule differentiation. The Lao script was standardized in the Mekong River valley after the various Tai principalities of the region were merged under Lan Xang in the 14th century. This script, sometimes known as Tai Noi, has changed little since its inception and continued use in the Lao-speaking regions of modern-day Laos, conversely, the Thai alphabet continued to evolve, but the scripts still share similarities. This script was derived locally from the Khmer script of Angkor with additional influence from Mon, traditionally, only secular literature were written with the Lao alphabet. Religious literature was written in Tua Tham, a Mon-based script that is still used for the Tai Khün, Tai Lue. Mystical, magical, and some literature was written in a modified version of the Khmer alphabet. Essentially Thai and Lao are almost typographic variants of other just as in the Javanese and Balinese scripts. The Lao and Thai alphabets share the same roots, but Lao has fewer characters and is written in a curvilinear fashion than Thai. However this is apparent today due to the communist party simplifying the spelling to be phonetic. There is speculation that the Lao and Thai script both derive from a common script due to the similarities between the scripts. When examining older forms of Thai scripts, many letters are almost identical to the Lao alphabet, some minority languages use separate writing systems, The Hmong have adopted the Roman Alphabet
14.
Thai numerals
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The Thai language lacks grammatical number. A count is expressed in the form of an uninflected noun followed by a number. In Thai, counting is kannap, the classifier, laksananam Variations to this pattern do occur, a partial list of Thai words that also classify nouns can be found in Wiktionary category, Thai classifiers. Thai sūn is written as oval 0 when using Arabic numerals, but a small circle ๐ when using traditional numerals and it is from Sanskrit śūnya, as are the alternate names for numbers one to four given below, but not the counting 1. Thai names for N +1 and the regular digits 2 through 9 as shown in the table, below, resemble those in Chinese varieties as spoken in Southern China, Thai and Lao words for numerals are almost identical, however, the numerical digits vary somewhat in shape. Shown below is a comparison between three languages using Cantonese and Minnan characters and pronunciations, the Thai transliteration uses the Royal Thai General System of Transcription. Sanskrit lakh designates the place value of a digit, which are named for the powers of ten, the place is lak nuai, tens place, lak sip, hundreds place, lak roi. The number one following any multiple of sip becomes et, the number ten is the same as Minnan 十. Numbers from twenty to twenty nine begin with yi sip, names of the lak sip for 30 to 90, and for the lak of 100,1000,10,000,100,000 and million, are almost identical to those of the like Khmer numerals. For the numbers twenty-one through twenty-nine, the part signifying twenty, yi sip, see the alternate numbers section below. The hundreds are formed by combining roi with the tens and ones values, for example, two hundred and thirty-two is song roi sam sip song. The words roi, phan, muen, and saen should occur with a preceding numeral, nueng never precedes sip, so song roi nueng sip is incorrect. Native speakers will sometimes use roi nueng with different tones on nueng to distinguish one hundred from one hundred, however, such distinction is often not made, and ambiguity may follow. To resolve this problem, if the number 101 is intended, numbers above a million are constructed by prefixing lan with a multiplier. For example, ten million is sip lan, and a trillion is lan lan, colloquially, decimal numbers are formed by saying chut where the decimal separator is located. For example,1.01 is nueng chut sun nueng, fractional numbers are formed by placing nai between the numerator and denominator or using x suan y to clearly indicate. For example, ⅓ is nueng nai sam or nueng suan sam, the word set can be omitted. The word khrueng is used for half and it precedes the measure word if used alone, but it follows the measure word when used with another number
15.
Chinese numerals
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Chinese numerals are words and characters used to denote numbers in Chinese. Today speakers of Chinese use three written numeral systems, the system of Arabic numerals used worldwide, and two indigenous systems, the more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These are shared with languages of the Chinese cultural sphere such as Japanese, Korean. The other indigenous system is the Suzhou numerals, or huama, a positional system and these were once used by Chinese mathematicians, and later in Chinese markets, such as those in Hong Kong before the 1990s, but have been gradually supplanted by Arabic numerals. The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals, similar to spelling-out numbers in English, it is not an independent system per se. Since it reflects spoken language, it not use the positional system as in Arabic numerals. There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands, there are two sets of characters for Chinese numerals, one for everyday writing and one for use in commercial or financial contexts known as dàxiě. A forger could easily change the everyday characters 三十 to 五千 just by adding a few strokes and that would not be possible when writing using the financial characters 參拾 and 伍仟. They are also referred to as bankers numerals, anti-fraud numerals, for the same reason, rod numerals were never used in commercial records. T denotes Traditional Chinese characters, S denotes Simplified Chinese characters, in the PLA, some numbers will have altered names when used for clearer radio communications. They are,0, renamed 洞 lit, hole 1, renamed 幺 lit. small 2, renamed 两 lit. Double 7, renamed 拐 lit. cane, kidnap, turn 9, hook For numbers larger than 10,000, similarly to the long and short scales in the West, there have been four systems in ancient and modern usage. The original one, with names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan. To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, the ROC government in Taiwan uses 兆 to mean 1012 in official documents. Numerals beyond 載 zài come from Buddhist texts in Sanskrit, but are found in ancient texts. Some of the words are still being used today. The following are characters used to denote small order of magnitude in Chinese historically, with the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest have fallen into disuse. In the Peoples Republic of China, the translations for the SI prefixes in 1981 were different from those used today, the Republic of China defined 百萬 as the translation for mega
16.
Suzhou numerals
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The Suzhou numerals, also known as Suzhou mazi or huama, is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numeral system is the only surviving variation of the rod numeral system, the rod numeral system is a positional numeral system used by the Chinese in mathematics. Suzhou numerals are a variation of the Southern Song rod numerals, Suzhou numerals were used as shorthand in number-intensive areas of commerce such as accounting and bookkeeping. At the same time, standard Chinese numerals were used in formal writing, Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have gradually been supplanted by Arabic numerals. This is similar to what had happened in Europe with Roman numerals used in ancient and medieval Europe for mathematics, nowadays, the Suzhou numeral system is only used for displaying prices in Chinese markets or on traditional handwritten invoices. In the Suzhou numeral system, special symbols are used for digits instead of the Chinese characters, the digits of the Suzhou numerals are defined between U+3021 and U+3029 in Unicode. An additional three code points starting from U+3038 were added later, the numbers one, two, and three are all represented by vertical bars. This can cause confusion when they next to each other. Standard Chinese ideographs are often used in this situation to avoid ambiguity, for example,21 is written as 〢一 instead of 〢〡 which can be confused with 3. The first character of such sequences is usually represented by the Suzhou numeral, the full numerical notations are written in two lines to indicate numerical value, order of magnitude, and unit of measurement. Following the rod system, the digits of the Suzhou numerals are always written horizontally from left to right. The first line contains the values, in this example. The second line consists of Chinese characters that represents the order of magnitude, in this case 十元 which stands for ten yuan. When put together, it is read as 40.22 yuan. Zero is represented by the character for zero, leading and trailing zeros are unnecessary in this system. This is very similar to the scientific notation for floating point numbers where the significant digits are represented in the mantissa. Also, the unit of measurement, with the first digit indicator, is aligned to the middle of the numbers row. In the Unicode standard version 3.0, these characters are incorrectly named Hangzhou style numerals, in the episode The Blind Banker of the 2010 BBC television series Sherlock, Sherlock Holmes erroneously refers to the number system as Hangzhou instead of the correct Suzhou
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Japanese numerals
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The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are based on the Chinese numerals. Two sets of pronunciations for the numerals exist in Japanese, one is based on Sino-Japanese readings of the Chinese characters, there are two ways of writing the numbers in Japanese, in Hindu-Arabic numerals or in Chinese numerals. The Hindu-Arabic numerals are often used in horizontal writing. Numerals with multiple On readings use the Go-on and Kan-on variants respectively, * The special reading 〇 maru is also found. It may be used when reading individual digits of a number one after another. A popular example is the famous 109 store in Shibuya, Tokyo which is read as ichi-maru-kyū and this usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. However, as a number, it is written as 0 or rei. Additionally, two and five are pronounced with a vowel in phone numbers Starting at 万, numbers begin with 一 if no digit would otherwise precede. That is,100 is just 百 hyaku, and 1000 is just 千 sen and this differs from Chinese as numbers begin with 一 if no digit would otherwise precede starting at 百. And, if 千 sen directly precedes the name of powers of myriad, 一 ichi is normally attached before 千 sen and that is,10,000,000 is normally read as 一千万 issenman. But if 千 sen does not directly precede the name of powers of myriad or if numbers are lower than 2,000 and that is,15,000,000 is read as 千五百万 sengohyakuman or 一千五百万 issengohyakuman, and 1,500 as 千五百 sengohyaku or 一千五百 issengohyaku. The numbers 4 and 9 are considered unlucky in Japanese,4, pronounced shi, is a homophone for death,9, the number 13 is sometimes considered unlucky, though this is a carryover from Western tradition. On the contrary, numbers 7 and sometimes 8 are considered lucky in Japanese, in modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in names, day-of-month names. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April, July, and September are called shi-gatsu, shichi-gatsu, the on readings are also used when shouting out headcounts. Intermediate numbers are made by combining elements, Tens from 20 to 90 are -jū as in 二十 to 九十. Hundreds from 200 to 900 are -hyaku, thousands from 2000 to 9000 are -sen
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Korean numerals
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The Korean language has two regularly used sets of numerals, a native Korean system and Sino-Korean system. For both native and Sino- Korean numerals, the teens are represented by a combination of tens, for instance,15 would be sib-o, but not usually il-sib-o in the Sino-Korean system, and yeol-daseot in native Korean. Twenty through ninety are likewise represented in this manner in the Sino-Korean system, while Native Korean has its own unique set of words. The grouping of large numbers in Korean follow the Chinese tradition of myriads rather than thousands, the Sino-Korean system is nearly entirely based on the Chinese numerals. The distinction between the two systems is very important. Everything that can be counted will use one of the two systems, but seldom both, Sino-Korean words are sometimes used to mark ordinal usage, yeol beon means ten times while sip beon means number ten. When denoting the age of a person, one will usually use sal for the native Korean numerals, for example, seumul-daseot sal and i-sib-o se both mean twenty-five-year-old. See also East Asian age reckoning, the Sino-Korean numerals are used to denote the minute of time. For example, sam-sib-o bun means __,35 or thirty-five minutes, the native Korean numerals are used for the hours in the 12-hour system and for the hours 0,00 to 12,00 in the 24-hour system. The hours 13,00 to 24,00 in the 24-hour system are denoted using both the native Korean numerals and the Sino-Korean numerals. For example, se si means 03,00 or 3,00 a. m. /p. m. for counting above 100, Sino-Korean words are used, sometimes in combination,101 can be baek-hana or baeg-il. The usual liaison and consonant-tensing rules apply, so for example, 예순여섯 yesun-yeoseot is pronounced like, beon, ho, cha, and hoe are always used with Sino-Korean or Arabic ordinal numerals. For example, Yihoseon is Line Number Two in a subway system. 906호 is Apt #906 in a mailing address,906 without ho is not used in spoken Korean to imply apartment number or office suite number. The special prefix je is usually used in combination with suffixes to designate a specific event in sequential things such as the Olympics, in commerce or the financial sector, some hanja for each Sino-Korean numbers are replaced by alternative ones to prevent ambiguity or retouching. For verbally communicating number sequences such as numbers, ID numbers, etc. especially over the phone. For the same reason, military transmissions are known to use mixed native Korean and Sino-Korean numerals, note 1, ^ Korean assimilation rules apply as if the underlying form were 십륙 |sip. ryuk|, giving sim-nyuk instead of the expected sib-yuk. Note 2, ^ ^ ^ ^ ^ These names are considered archaic, note 3, ^ ^ ^ ^ ^ ^ ^ The numbers higher than 1020 are not usually used
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Vietnamese numerals
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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 are used in modern English, Sino-Vietnamese words are also used for units of ten thousand or above, where native vocabulary was lacking. Among the languages of the Chinese cultural sphere, Japanese and Korean both use two systems, one native and one Chinese-based. The Chinese-based vocabulary is the one in common use, in Vietnamese, on the other hand, the Chinese-based system is not in everyday use. Numbers from 1 to 1000 are expressed using native Vietnamese vocabulary, in the modern Vietnamese writing system, numbers are written in the romanized script quốc ngữ or Arabic numerals. Prior to the 20th century Vietnam officially used Classical Chinese as a written language, for non-official purposes Vietnamese also had a writing system known as Hán-Nôm. Under this system, Sino-Vietnamese numbers were written in Hán tự, basic features of the Vietnamese numbering system include the following, Unlike other sinoxenic numbering systems, Vietnamese separates place values in thousands rather than myriads. The Sino-Vietnamese numbers are not in frequent use in modern Vietnamese, number values for these words follow usage in Ancient China, with each numeral increasing tenfold in digit value, 億 being the number for 105, 兆 for 106, et cetera. As a result, the value of triệu differs from modern Chinese 兆, outside of fixed Sino-Vietnamese expressions, Sino-Vietnamese words are usually used in combination with native Vietnamese words. For instance, mười triệu combines native mười and Sino-Vietnamese triệu, the following table is an overview of the basic Vietnamese numeric figures, provided in both Native and Sino-Viet forms. For each number, the form that is commonly used is highlighted. Where there are differences between the Hanoi and Saigon dialects of Vietnamese, readings between each are differentiated below within the notes, when the number 1 appears after 20 in the unit digit, the pronunciation changes to mốt. When the number 4 appears after 20 in the digit, it is more common to use Sino-Viet tư／四. When the number 5 appears after 10 in the unit digit, when mười appears after 20, the pronunciation changes to mươi. Vietnamese ordinal numbers are preceded by the prefix thứ, which is a Sino-Viet word which corresponds to 次. For the ordinal numbers of one and four, the Sino-Viet readings nhất／一 and tư／四 are more commonly used, in all other cases, the native Vietnamese number is used. Chinese numerals Japanese numerals Korean numerals
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Counting rods
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Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China, Japan, Korea, and Vietnam. They are placed horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals and they are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period to the 16th century. Counting rods were used by ancient Chinese for more two thousand years. In 1954, forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, in 1973, archeologists unearthed a number of wood scripts from a Han dynasty tomb in Hubei. On one of the scripts was written, “当利二月定算”. This is one of the earliest examples of using counting rod numerals in writing, in 1976, a bundle of Western Han counting rods made of bones was unearthed from Qianyang County in Shaanxi. The use of counting rods must predate it, Laozi said a good calculator doesnt use counting rods, the Book of Han recorded, they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces. At first calculating rods were round in section, but by the time of the Sui dynasty triangular rods were used to represent positive numbers. After the abacus flourished, counting rods were abandoned except in Japan, counting rods represent digits by the number of rods, and the perpendicular rod represents five. To avoid confusion, vertical and horizontal forms are alternately used, generally, vertical rod numbers are used for the position for the units, hundreds, ten thousands, etc. while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written in Sunzi Suanjing that one is vertical, ten is horizontal, red rods represent positive numbers and black rods represent negative numbers. Ancient Chinese clearly understood negative numbers and zero, though they had no symbol for the latter, later, a go stone was sometimes used to represent zero. This alternation of vertical and horizontal rod numeral form is important to understanding written transcription of rod numerals on manuscripts correctly. In the same manuscript,405 was transcribed as, with a space in between for obvious reasons, and could in no way be interpreted as 45. In other words, transcribed rod numerals may not be positional, the value of a number depends on its physical position on the counting board. A9 at the rightmost position on the stands for 9. Moving the batch of rods representing 9 to the one position gives 9 or 90