Tamil numerals, refers to the numeral system of the Tamil language used in Tamil Nadu and Singapore, as well as by the other Tamil-speaking populations around the world including Sri Lanka, Mauritius, Réunion, South Africa, other emigrant communities around the world. Old Tamil possesses a special numerical character for zero and it is read as andru, but yet Modern Tamil renounces the use of its native character and uses Arabic, 0. Modern Tamil words for zero include சுழியம் or பூச்சியம். Tamil has a numeric prefix for each number from 1 to 9, which can be added to the words for the powers of ten to form multiples of them. For instance, the word for fifty, ஐம்பது is a combination of ஐ and பத்து; 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 void in the Tamil language except for some Hindu and Christian religious references, example'அட்ட இலட்சுமிகள்' in a Hindu context, or'ஏக பாலன்' in a Christian context.
However, it should be noted, that in religious contexts Tamil language is more preferred for its more poetic nature and low incidence of consonant clusters. Unlike other Indian writing systems, Tamil has distinct digits for 10, 100, 1000, it has distinct characters for other number-based aspects of day-to-day life. There are two numeral systems that can be used in the Tamil language: the Tamil system, as followsThe following are the traditional numbers of the Ancient Tamil Country, Tamizhakam. Proposals to encode Tamil fractions and symbols to Unicode were submitted; as of version 12.0, Tamil characters used for fractional values in traditional accounting practices were added to the Unicode Standard. 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. Common fractions have names allocated to them, these names are used rather than the above method.
Other fractions include: ^ Aṇu was considered as the lowest fraction by ancient Tamils as size of smallest physical object. This term went to Sanskrit to refer directly to atoms. 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; these words are added after a number to form percentages. For instance, four percent is நான்கு சதவீதம் or நான்கு விழுக்காடு. Percentage symbol is recognised and used. Ordinal numbers are formed by adding the suffix -ஆம் after the number, except for'First'; 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. This song is a list of each number with a concept its associated with; as the antique classical language of the Dravidian languages, Tamil numerals influenced and shaped the numerals of the others in the family. The following table compares the main Dravidian languages. Tamil through the Pallava script which itself through the Kawi script, Khmer script and other South-east Asian scripts has shaped the numeral grapheme of most South-east Asian languages.
Before the Government of India unveiled ₹ as the new rupee symbol, people in Tamil Nadu used the Tamil letter ௹ as the symbol. This symbol continues to be used as rupee symbol by Indian Tamils out of habit, it is used by Tamils in Sri Lanka ௳ is known as the Pillaiyar Suzhi. The Tamil numbers used symbols; the Sanskrit numerals are as follows: 1- ekam 2- dhwey 3- thrini 4- chathwari 5- pancha 6- shad 7- saptha 8- ashta 9- nava 10- dhasa Tamil script Tamil units of measurement
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
Counting rods are small bars 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any rational number; the written forms based on them are called rod numerals. 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. Chinese arithmeticians used counting rods well over two thousand years ago. In 1954 forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, Hunan. In 1973 archeologists unearthed a number of wood scripts from a tomb in Hubei dating from the period of the Han dynasty. On one of the wooden 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-era counting rods made of bones was unearthed from Qianyang County in Shaanxi; the use of counting rods must predate it. 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 cross-section, but by the time of the Sui dynasty mathematicians used triangular rods to represent positive numbers and rectangular rods for negative numbers. After the abacus flourished, counting rods were abandoned except in Japan, where rod numerals developed into a symbolic notation for algebra. Counting rods represent digits by the number of rods, the perpendicular rod represents five. To avoid confusion and horizontal forms are alternately used. Vertical rod numbers are used for the position for the units, ten thousands, etc. while horizontal rod numbers are used for the tens, hundred thousands etc. It is written in Sunzi Suanjing that "one is vertical, ten is horizontal". Red rods represent black rods represent negative numbers. Ancient Chinese understood negative numbers and zero, though they had no symbol for the latter; the Nine Chapters on the Mathematical Art, composed in the first century CE, stated " subtract same signed numbers, add different signed numbers, subtract a positive number from zero to make a negative number, subtract a negative number from zero to make a positive number".
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. For instance, in Licheng suanjin, 81 was transcribed as, 108 was transcribed as. In the same manuscript, 405 was transcribed as, with a blank space in between for obvious reasons, could in no way be interpreted as "45". In other words, transcribed rod numerals may not be positional, but on the counting board, they are positional. is an exact image of the counting rod number 405 on a table top or floor. The value of a number depends on its physical position on the counting board. A 9 at the rightmost position on the board stands for 9. Moving the batch of rods representing 9 to the left one position gives 9 or 90. Shifting left again to the third position gives 9 or 900; each time one shifts a number one position to the left, it is multiplied by 10. Each time one shifts a number one position to the right, it is divided by 10.
This applies to multiple-digit numbers. Song dynasty mathematician Jia Xian used hand-written Chinese decimal orders 步十百千萬 as rod numeral place value, as evident from a facsimile from a page of Yongle Encyclopedia, he arranged 七萬一千八百二十四 as 七一八二四 萬千百十步He treated the Chinese order numbers as place value markers, 七一八二四 became place value decimal number. He wrote the rod numerals according to their place value: In Japan, mathematicians put counting rods on a counting board, a sheet of cloth with grids, used only vertical forms relying on the grids. An 18th-century Japanese mathematics book has a checker counting board diagram, with the order of magnitude symbols "千百十一分厘毛“. Examples: Rod numerals are a positional numeral system made from shapes of counting rods. Positive numbers are written as they are and the negative numbers are written with a slant bar at the last digit; the vertical bar in the horizontal forms 6–9 are drawn shorter to have the same character height. A circle is used for 0. Many historians think it was imported from Indian numerals by Gautama Siddha in 718, but some think it was created from the Chinese text space filler "□", others think that the Indians acquired it from China, because it resembles a Confucian philosophical symbol for nothing.
In the 13th century, Southern Song mathematicians changed digits for 4, 5, 9 to reduce strokes. The new horizontal forms transformed into Suzhou numerals. Japanese continued to use the traditional forms. Examples: In Japan, Seki Takakazu developed the rod num
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
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
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal positional numeral system; the numerals are made up of three symbols. For example, thirteen is written as three dots in a horizontal row above two horizontal bars. With these three symbols each of the twenty vigesimal digits could be written. Numbers after 19 were written vertically in powers of twenty; the Mayan used powers of twenty, just as the Hindu–Arabic numeral system uses powers of tens. For example, thirty-three would be written as one dot, above three dots atop two bars; the first dot represents "one twenty" or "1×20", added to three dots and two bars, or thirteen. Therefore, + 13 = 33. Upon reaching 202 or 400, another row is started; the number 429 would be written as one dot above one dot above four dots and a bar, or + + 9 = 429. Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures; the face glyph for a number represents the deity associated with the number.
These face number glyphs were used, are seen on some of the most elaborate monumental carving. Adding and subtracting numbers below 20 using Maya numerals is simple. Addition is performed by combining the numeric symbols at each level: If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher row. With subtraction, remove the elements of the subtrahend symbol from the minuend symbol: If there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol, being worked on; the "Long Count" portion of the Maya calendar uses a variation on the vigesimal numbering. In the second position, only the digits up to 17 are used, the place value of the third position is not 20×20 = 400, as would otherwise be expected, but 18×20 = 360, so that one dot over two zeros signifies 360.
This is because 360 is the number of days in a year. Subsequent positions use all twenty digits and the place values continue as 18×20×20 = 7,200 and 18×20×20×20 = 144,000, etc; every known example of large numbers in the Maya system uses this'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system. Several Mesoamerican cultures used similar numerals and base-twenty systems and the Mesoamerican Long Count calendar requiring the use of zero as a place-holder; the earliest long count date is from 36 BC. Since the eight earliest Long Count dates appear outside the Maya homeland, it is assumed that the use of zero and the Long Count calendar predated the Maya, was the invention of the Olmec. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was not an Olmec discovery.
Mayan numerals were added to the Unicode Standard in June, 2018 with the release of version 11.0. The Unicode block for Mayan Numerals is U+1D2E0–U+1D2FF: Maya Mathematics - online converter from decimal numeration to Maya numeral notation. Anthropomorphic Maya numbers - online story of number representations. BabelStone Mayan Numerals - free font for Unicode Mayan numeral characters
The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals in the late 2nd century BCE; the current numeral system is known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from c. 800 BC in the so-called Samaria ostraca and sometimes known as Hebrew-Aramaic numerals derived from the Egyptian Hieratic numerals. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BC. In this system, there is no notation for zero, the numeric values for individual letters are added together; each unit is assigned a separate letter, each tens a separate letter, the first four hundreds a separate letter. The hundreds are represented by the sum of two or three letters representing the first four hundreds.
To represent numbers from 1,000 to 999,999, the same letters are reused to serve as thousands, tens of thousands, hundreds of thousands. Gematria uses these transformations extensively. In Israel today, the decimal system of Arabic numerals is used in all cases; the Hebrew numerals are used only in special cases, such as when using the Hebrew calendar, or numbering a list, much as Roman numerals are used in the West. The Hebrew language has names for common numbers. Letters of the Hebrew alphabet are used to represent numbers in a few traditional contexts, for example in calendars. In other situations Arabic numerals are used. Cardinal and ordinal numbers must agree in gender with the noun. If there is no such noun, the feminine form is used. For ordinal numbers greater than ten the cardinal is used and numbers above the value 20 have no gender. Note: For ordinal numbers greater than 10, cardinal numbers are used instead. Note: For numbers greater than 20, gender does not apply. Numbers greater than million were represented by the long scale.
Cardinal and ordinal numbers must agree in gender with the noun. If there is no such noun, the feminine form is used. Ordinal numbers must agree in number and definite status like other adjectives; the cardinal number precedes the noun, except for the number one. The number two is special: shnayim and shtayim become shney and shtey when followed by the noun they count. For ordinal numbers greater than ten the cardinal is used; the Hebrew numeric system operates on the additive principle in which the numeric values of the letters are added together to form the total. For example, 177 is represented as קעז which corresponds to 100 + 70 + 7 = 177. Mathematically, this type of system requires 27 letters. In practice the last letter, tav is used in combination with itself and/or other letters from kof onwards, to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes extended to 27 by using 5 sofit forms of the Hebrew letters. By convention, the numbers 15 and 16 are represented as ט״ו and ט״ז in order to refrain from using the two-letter combinations י-ה and י-ו, which are alternate written forms for the Name of God in everyday writing.
In the calendar, this manifests every full moon. Combinations which would spell out words with negative connotations are sometimes avoided by switching the order of the letters. For instance, 744 which should be written as תשמ״ד might instead be written as תשד״מ or תמש״ד; the Hebrew numeral system has sometimes been extended to include the five final letter forms—ך, ם, ן, ף and ץ —which are used to indicate the numbers from 500 to 900. The ordinary forms for 500 to 900 are: ת״ק, ת״ר, ת״ש, ת״ת and תת״ק. Gershayim are inserted before the last letter to indicate that the sequence of letters represents a number rather than a word; this is used in the case. A single Geresh is appended after a single letter to indicate that the letter represents a number rather than a word; this is used in the case. Note that Geresh and Gershayim indicate "not a word." Context determines whether they indicate a number or something else. An alternative method found in old manuscripts and still found on modern-day tombstones is to put a dot above each letter of the number.
In print, Arabic numerals are emplo