Suzhou numerals
The Suzhou numerals known as Suzhou mazi, is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numerals are known as huama, jingzima and shangma; 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, akin to spelling out the numbers in English. Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have 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 and commerce. 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 +3029 in Unicode. An additional three code points starting from U+3038 were added later; the numbers one and three are all represented by vertical bars. This can cause confusion. Standard Chinese ideographs are 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 represented by the Suzhou numeral, while the second character is represented by the Chinese ideograph. The digits are positional; the full numerical notations are written in two lines to indicate numerical value, order of magnitude, unit of measurement. Following the rod numeral system, the digits of the Suzhou numerals are always written horizontally from left to right when used within vertically written documents; the first line contains the numerical values, in this example, "〤〇〢二" stands for "4022".
The second line consists of Chinese characters that represents the order of magnitude and unit of measurement of the first digit in the numerical representation. In this case "十元" which stands for "ten yuan"; when put together, it is read as "40.22 yuan". Possible characters denoting order of magnitude include: qiān for thousand bǎi for hundred shí for ten blank for oneOther possible characters denoting unit of measurement include: yuán for dollar máo or for 10 cents lǐ for the Chinese mile any other Chinese measurement unitNotice that the decimal point is implicit when the first digit is set at the ten position. Zero is represented by the character for zero. Leading and trailing zeros are unnecessary in this system; this is similar to the modern scientific notation for floating point numbers where the significant digits are represented in the mantissa and the order of magnitude is specified in the exponent. 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 Unicode standard 4.0, an erratum was added which stated: The Suzhou numerals are special numeric forms used by traders to display the prices of goods. The use of "HANGZHOU" in the names is a misnomer. All references to "Hangzhou" in the Unicode standard have been corrected to "Suzhou" except for the character names themselves, which cannot be changed once assigned, according to the Unicode Stability Policy. 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."
Japanese numerals
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 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 readings of the Chinese characters and the other is based on the Japanese yamato kotoba. There are two ways of writing the numbers in Japanese: in Chinese numerals; the Arabic numerals are more used in horizontal writing, the Chinese numerals are more common in vertical writing. Most numbers have two readings, one derived from Chinese used for cardinal numbers and a native Japanese reading used somewhat less formally for numbers up to 10. In some cases the Japanese reading is preferred for all uses. * The special reading 〇 maru is found. It may be optionally used when reading individual digits of a number one after another, instead of as a full number. A popular example is the famous 109 store in Shibuya, Tokyo, read as ichi-maru-kyū.
This usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. It means a circle. However, as a number, it is only written as rei. Additionally and five are pronounced with a long vowel in phone numbers. Starting at 万, numbers begin with 一; that is, 100 is just 百 hyaku, 1000 is just 千 sen, but 10,000 is 一万 ichiman, not just *man. 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 attached before 千 sen, which yields 一千 issen; that is, 10,000,000 is 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, attaching 一 ichi is optional; that is, 15,000,000 is read as 千五百万 sengohyakuman or 一千五百万 issengohyakuman, 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. See tetraphobia; the number 13 is sometimes considered unlucky.
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 month names, day-of-month names, fixed phrases. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April and September are called shi-gatsu, shichi-gatsu, ku-gatsu respectively. The on readings are used when shouting out headcounts. Intermediate numbers are made by combining these 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". There are some phonetic modifications to larger numbers involving voicing or gemination of certain consonants, as occurs in Japanese: e.g. roku "six" and hyaku "hundred" yield roppyaku "six hundred". * This applies to multiples of 10. Change ending -jū to -jutchō or -jukkei. ** This applies to multiples of 100. Change ending -ku to -kkei.
In large numbers, elements are combined from largest to smallest, zeros are implied. Beyond the basic cardinals and ordinals, Japanese has other types of numerals. Distributive numbers are formed from a cardinal number, a counter word, the suffix -zutsu, as in hitori-zutsu. Following Chinese tradition, large numbers are created by grouping digits in myriads rather than the Western thousands: Variation is due to Jinkōki, Japan's oldest mathematics text; the initial edition was published in 1627. It had many errors. Most of these were fixed in the 1631 edition. In 1634 there was yet another edition; the above variation is due to inconsistencies in the latter two editions. Examples: 1 0000: 一万 983 6703: 九百八十三万 六千七百三 20 3652 1801: 二十億 三千六百五十二万 千八百一 However, numbers written in Arabic numerals are separated by commas every three digits following English-speaking convention. If Arabic numbers and kanji are used in combination, Western orders of magnitude may be used for numbers smaller than 10,000. In Japanese, when long numbers are written out in kanji, zeros are omitted for all powers of ten.
Hence 4002 is 四千二. However, when reading out a statement of accounts, for example, the skipped digit or digits are sometimes indicated by tobi or tonde: e.g. yon-sen tobi ni or yon-sen tonde ni instead of the normal yon-sen ni. Japanese has two systems of numerals for decimal fractions, they are no longer in general use, but are still used in some instances such as batting and fielding averages of baseball players, winning percentages for sports teams, in some idiomatic phrases, when repr
Hindu–Arabic numeral system
The Hindu–Arabic numeral system is a positional decimal numeral system, is the most common system for the symbolic representation of numbers in the world. It was invented between the 4th centuries by Indian mathematicians; the system was adopted in Arabic mathematics by the 9th century. Influential were the books of Al-Kindi; the system spread to medieval Europe by the High Middle Ages. The system is based upon ten glyphs; the symbols 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; these symbol sets can be divided into three main families: Western Arabic numerals used in the Greater Maghreb and in Europe, Eastern Arabic numerals used in the Middle East, the Indian numerals used in the Indian subcontinent. The Hindu-Arabic numerals were invented by mathematicians in India. Perso-Arabic mathematicians called them "Hindu numerals", they came to be called "Arabic numerals" in Europe, because they were introduced to the West by Arab merchants.
The Hindu–Arabic system is designed for positional notation in a decimal system. In a more developed form, positional notation uses a decimal marker, a symbol for "these digits recur ad infinitum". In modern usage, this latter symbol is a vinculum. In this more developed form, the numeral system can symbolize any rational number using only 13 symbols. Although found in text written with the Arabic abjad, numbers written with these numerals place the most-significant digit to the left, so they read from left to right; the requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, most of which developed from the Brahmi numerals; the symbols used to represent the system have split into various typographical variants since the Middle Ages, arranged in three main groups: The widespread Western "Arabic numerals" used with the Latin and Greek alphabets in the table, descended from the "West Arabic numerals" which were developed in al-Andalus and the Maghreb.
The "Arabic–Indic" or "Eastern Arabic numerals" used with Arabic script, developed in what is now Iraq. A variant of the Eastern Arabic numerals is used in Urdu; the Indian numerals in use with scripts of the Brahmic family in India and Southeast Asia. Each of the dozen major scripts of India has its own numeral glyphs; as in many numbering systems, the numerals 1, 2, 3 represent simple tally marks. After three, numerals tend to become more complex symbols. Theorists believe that this is because it becomes difficult to instantaneously count objects past three; the Brahmi numerals at the basis of the system predate the Common Era. They replaced the earlier Kharosthi numerals used since the 4th century BC. Brahmi and Kharosthi numerals were used alongside one another in the Maurya Empire period, both appearing on the 3rd century BC edicts of Ashoka. Buddhist inscriptions from around 300 BC use the symbols that became 1, 4, 6. One century their use of the symbols that became 2, 4, 6, 7, 9 was recorded.
These Brahmi numerals are the ancestors of the Hindu–Arabic glyphs 1 to 9, but they were not used as a positional system with a zero, there were rather separate numerals for each of the tens. The actual numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, younger than the Brahmi numerals; the place-value system is used in the Bakhshali Manuscript. Although date of the composition of the manuscript is uncertain, the language used in the manuscript indicates that it could not have been composed any than 400; the development of the positional decimal system takes its origins in Hindu mathematics during the Gupta period. Around 500, the astronomer Aryabhata uses the word kha to mark "zero" in tabular arrangements of digits; the 7th century Brahmasphuta Siddhanta contains a comparatively advanced understanding of the mathematical role of zero. The Sanskrit translation of the lost 5th century Prakrit Jaina cosmological text Lokavibhaga may preserve an early instance of positional use of zero.
These Indian developments were taken up in Islamic mathematics in the 8th century, as recorded in al-Qifti's Chronology of the scholars. The numeral system came to be known to both the Persian mathematician Khwarizmi, who wrote a book, On the Calculation with Hindu Numerals in about 825, the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Hindu Numerals around 830; these earlier texts did not use the Hindu numerals. Kushyar ibn L
Quipu
Quipu, or talking knots, were recording devices fashioned from strings used by a number of cultures in the region of Andean South America. Knotted strings were used by many other cultures such as the ancient Chinese and native Hawaiians, but such practices should not be confused with the quipu, which refers only to the Andean device. A quipu consisted of cotton or camelid fiber strings; the Inca people used them for collecting data and keeping records, monitoring tax obligations, properly collecting census records, calendrical information, for military organization. The cords stored numeric and other values encoded as knots in a base ten positional system. A quipu could have thousands of cords; the configuration of the quipus has been "compared to string mops." Archaeological evidence has shown the use of finely carved wood as a supplemental, more sturdy, base to which the color-coded cords would be attached. A small number have survived. Objects that can be identified unambiguously as quipus first appear in the archaeological record in the first millennium AD.
They subsequently played a key part in the administration of the Kingdom of Cusco and Tawantinsuyu, the empire controlled by the Inca ethnic group, flourishing across the Andes from c. 1100 to 1532 AD. As the region was subsumed under the invading Spanish Empire, the use of the quipu faded from use, to be replaced by European writing and numeral systems. However, in several villages, quipu continued to be important items for the local community, albeit for ritual rather than practical use, it is unclear as to where and how many intact quipus still exist, as many have been stored away in mausoleums. Quipu is the most common spelling in English. Khipu is the word for "knot" in Cusco Quechua. In most Quechua varieties, the term is kipu; the word "khipu", meaning "knot" or "to knot", comes from the Quechua language word: quipu, 1704, the "lingua franca and language of administration" of Tawantin Suyu. Most information recorded on the quipus consists of numbers in a decimal system. In the early years of the Spanish conquest of Peru, Spanish officials relied on the quipus to settle disputes over local tribute payments or goods production.
Quipucamayocs could be summoned to court, where their bookkeeping was recognised as valid documentation of past payments. Some of the knots, as well as other features, such as color, are thought to represent non-numeric information, which has not been deciphered, it is thought that the system did not include phonetic symbols analogous to letters of the alphabet. However Gary Urton has suggested that the quipus used a binary system which could record phonological or logographic data; the lack of a clear link between any indigenous Peruvian languages and the quipus has led to the supposition that quipus are not a glottographic writing system and have no phonetic referent. Frank Salomon at the University of Wisconsin has argued that quipus are a semasiographic language, a system of representative symbols – such as music notation or numerals – that relay information but are not directly related to the speech sounds of a particular language; the Khipu Database Project, begun by Gary Urton, may have decoded the first word from a quipu–the name of a village, Puruchuco–which Urton believes was represented by a three-number sequence, similar to a ZIP code.
If this conjecture is correct, quipus are the only known example of a complex language recorded in a 3-D system. Most Sabine Hyland has made the first phonetic decipherment of a quipu, challenging the assumption that quipus do not represent information phonetically. After being contacted by local woman Meche Moreyra Orozco, the head of the Association of Collatinos in Lima, Hyland was granted access to the epistolary quipus of San Juan de Collata; these quipus were exchanged during an 18th century rebellion against the Spanish government. A combination of color and ply direction leads to a total of 95 combinations in these quipus, within the range of a logosyllabic writing system. Exchanging information about the rebellion through quipus would have prevented the Spanish authorities from understanding the messages if they were intercepted, the Collata quipus are non-numeric. With the help of local leaders, who described the quipu as "a language of animals", Hyland was able to translate the names of the two ayllus, or family lineages, who received and sent the quipu.
The translation relied on phonetic references to the animal fibers and colors of the relevant quipu cords. Future research will attempt to determine whether Hyland's findings are applicable to quipus from the Inca period and earlier. Marcia and Robert Ascher, after having analyzed several hundred quipus, have shown that most information on quipus is numeric, these numbers can be read; each cluster of knots is a digit, there are three main types of knots: simple overhand knots. In the Aschers’ system, a fourth type of knot—figure-of-eight knot with an extra twist—is referred to as "EE". A number is represented as a sequence of knot clusters in base 10. Powers of ten are shown by position along the string, this position is aligned between successive strands. Digits in positions for 10 and higher powers are represented by clusters of simple knots. Digits in the "ones" position are represented by long knots; because of the way the knots are tied, the digit 1 cannot be shown this wa
Binary number
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: "0" and "1". The base-2 numeral system is a positional notation with a radix of 2; each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by all modern computers and computer-based devices; the modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt and India. Leibniz was inspired by the Chinese I Ching; the scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions. Horus-Eye fractions are a binary numbering system for fractional quantities of grain, liquids, or other measures, in which a fraction of a hekat is expressed as a sum of the binary fractions 1/2, 1/4, 1/8, 1/16, 1/32, 1/64.
Early forms of this system can be found in documents from the Fifth Dynasty of Egypt 2400 BC, its developed hieroglyphic form dates to the Nineteenth Dynasty of Egypt 1200 BC. The method used for ancient Egyptian multiplication is closely related to binary numbers. In this method, multiplying one number by a second is performed by a sequence of steps in which a value is either doubled or has the first number added back into it; this method can be seen in use, for instance, in the Rhind Mathematical Papyrus, which dates to around 1650 BC. The I Ching dates from the 9th century BC in China; the binary notation in the I Ching is used to interpret its quaternary divination technique. It is based on taoistic duality of yin and yang.eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, although he did not intend his arrangement to be used mathematically.
Viewing the least significant bit on top of single hexagrams in Shao Yong's square and reading along rows either from bottom right to top left with solid lines as 0 and broken lines as 1 or from top left to bottom right with solid lines as 1 and broken lines as 0 hexagrams can be interpreted as sequence from 0 to 63. The Indian scholar Pingala developed a binary system for describing prosody, he used binary numbers in the form of long syllables, making it similar to Morse code. Pingala's Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter; the binary representations in Pingala's system increases towards the right, not to the left like in the binary numbers of the modern, Western positional notation. The residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Asia. Sets of binary combinations similar to the I Ching have been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy.
In the late 13th century Ramon Llull had the ambition to account for all wisdom in every branch of human knowledge of the time. For that purpose he developed a general method or ‘Ars generalis’ based on binary combinations of a number of simple basic principles or categories, for which he has been considered a predecessor of computing science and artificial intelligence. In 1605 Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could be encoded as scarcely visible variations in the font in any random text. For the general theory of binary encoding, he added that this method could be used with any objects at all: "provided those objects be capable of a twofold difference only. John Napier in 1617 described a system he called location arithmetic for doing binary calculations using a non-positional representation by letters. Thomas Harriot investigated several positional numbering systems, including binary, but did not publish his results.
The first publication of the system in Europe was by Juan Caramuel y Lobkowitz, in 1700. Leibniz studied binary numbering in 1679. Leibniz's system uses 1, like the modern binary numeral system. An example of Leibniz's binary numeral system is as follows: 0 0 0 1 numerical value 20 0 0 1 0 numerical value 21 0 1 0 0 numerical value 22 1 0 0 0 numerical value 23Leibniz interpreted the hexagrams of the I Ching as evidence of binary calculus; as a Sinophile, Leibniz was aware of
Chinese numerals
Chinese numerals are words and characters used to denote numbers in Chinese. Today, speakers of Chinese use three written numeral systems: the system of Hindu-Arabic numerals used worldwide, 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 other languages of the Chinese cultural sphere such as Japanese and Vietnamese. Most people and institutions in China and Taiwan use the Hindu-Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance for writing amounts on checks, some ceremonial occasions, some boxes, on commercials; the other indigenous system is the Suzhou numerals, or huama, a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, in Chinese markets, such as those in Hong Kong before the 1990s, but have been supplanted by Hindu-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 does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not. There are characters representing the numbers zero through nine, other characters representing larger numbers such as tens, thousands and so on. There are two sets of characters for Chinese numerals: one for everyday writing, known as xiǎoxiě, one for use in commercial or financial contexts, known as dàxiě; the latter arose because the characters used for writing numerals are geometrically simple, so using those numerals cannot prevent forgeries in the same way spelling numbers out in English would. A forger could change the everyday characters 三十 to 五千 just by adding a few strokes; that would not be possible when writing using the financial characters 叁拾 and 伍仟. They are referred to as "banker's numerals", "anti-fraud numerals", or "banker's anti-fraud numerals".
For the same reason, rod numerals were never used in commercial records. T denotes Traditional Chinese characters. In the People's Liberation Army of the People's Republic of China, 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, turn 9: renamed 勾 lit. Hook For numbers larger than 10,000 to the long and short scales in the West, there have been four systems in ancient and modern usage; the original one, with unique names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan, Wujing suanshu. In modern Chinese only the second system is used, in which the same ancient names are used, but each represents a number 10,000 times the previous: In practice, this situation does not lead to ambiguity, with the exception of 兆, which means 1012 according to the system in common usage throughout the Chinese communities as well as in Japan and Korea, but has been used for 106 in recent years.
To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿 or 太 instead. Due to this, combinations of 万 and 亿 are used instead of the larger units of the traditional system as well, for example 亿亿 instead of 京; the ROC government in Taiwan uses 兆 to mean 1012 in official documents. Numerals beyond 載 zǎi come from Buddhist texts in Sanskrit, but are found in ancient texts; some of the following words may have transferred meanings. 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 People's Republic of China, the early translation for the SI prefixes in 1981 was different from those used today; the larger and smaller Chinese numerals were defined as translation for the SI prefixes as mega, tera, exa, nano, femto, resulting in the creation of yet more values for each numeral.
The Republic of China defined 百萬 as the translation for 兆 as the translation for tera. This translation is used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz". Today, the governments of both Taiwan use phonetic transliterations for the SI prefixes. However, the governments have each chosen different Chinese characters for certain prefixes; the following table lists the two different standards together with the early translation. Multiple-digit numbers are constructed using a multiplicative principle. In Mandarin, the multiplier 兩 is used rather than 二 for all numbers 200 and greater with the "2" numeral. Use of both 兩 or 二 are acceptabl
Cyrillic numerals
Cyrillic numerals are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire in the late 10th century. It was used by South and East Slavic peoples; the system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. Cyrillic numbers played a role in Peter the Great's currency reform plans, with silver wire kopecks issued after 1696 and mechanically minted coins issued between 1700 and 1722 inscribed with the date using Cyrillic numerals. By 1725, Russian Imperial coins had transitioned to Arabic numerals; the Cyrillic numerals may still be found in books written in the Church Slavonic language. The system is a quasi-decimal alphabetic system, equivalent to the Ionian numeral system but written with the corresponding graphemes of the Cyrillic script; the order is based on the original Greek alphabet rather than the standard Cyrillic alphabetical order. A separate letter is assigned to each unit, each multiple of ten, each multiple of one hundred.
To distinguish numbers from text, a titlo is sometimes drawn over the numbers, or they are set apart with dots. The numbers are written as pronounced in Slavonic from the high value position to the low value position, with the exception of 11 through 19, which are written and pronounced with the ones unit before the tens. Examples: – 1706 – 7118To evaluate a Cyrillic number, the values of all the figures are added up: for example, ѰЗ is 700 + 7, making 707. If the number is greater than 999, the thousands sign is used to multiply the number's value: for example, ҂Ѕ is 6000, while ҂Л҂В is parsed as 30,000 + 2000, making 32,000. To produce larger numbers, a modifying sign is used to encircle the number being multiplied. Two scales existed in such cases, one giving a new name and sign every order of magnitude, the other, each squaring except for the end Glagolitic numerals are similar to Cyrillic numerals except that numeric values are assigned according to the native alphabetic order of the Glagolitic alphabet.
Glyphs for the ones and hundreds values are combined to form more precise numbers, for example, ⰗⰑⰂ is 500 + 80 + 3 or 583. As with Cyrillic numerals, the numbers 11 through 19 are written with the ones digit before the glyph for 10. Whereas Cyrillic numerals use modifying signs for numbers greater than 999, some documents attest to the use of Glagolitic letters for 1000 through 6000, although the validity of 3000 and greater is questioned. Early Cyrillic alphabet Glagolitic alphabet Relationship of Cyrillic and Glagolitic scripts Greek numerals Combining Cyrillic Millions