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Indian Numerals
INDIAN NUMERALS are the symbols representing numbers in India. These numerals are generally used in the context of the decimal Hindu–Arabic numeral system
Hindu–Arabic numeral system
, and are distinct from, though related by descent to Arabic numerals
Arabic numerals
. CONTENTS * 1 Devanagari
Devanagari
numerals and their Hindi
Hindi
and Sanskrit
Sanskrit
names * 2 Other North Indic scripts * 3 South Indic scripts * 4 History * 5 See also * 6 References DEVANAGARI NUMERALS AND THEIR HINDI AND SANSKRIT NAMESBelow is a list of the Indian numerals
Indian numerals
in their modern Devanagari form, the corresponding Hindu-Arabic (European) equivalents, their Hindi
Hindi
and Sanskrit
Sanskrit
pronunciation, and translations in some languages
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Dzongkha Numerals
Dzongkha , the national language of Bhutan
Bhutan
, has two numeral systems, one vigesimal (base 20), and a modern decimal system. The vigesimal system remains in robust use. Ten is an auxiliary base: the teens are formed with ten and the numerals 1–9. VIGESIMAL 1 ciː 11 cu-ci 2 ˈɲiː 12 cu-ɲi 3 sum 13 cu-sum 4 ʑi 14 cu-ʑi 5 ˈŋa 15 ce-ŋa 6 ɖʱuː 16 cu-ɖu 7 dyn 17 cup-dỹ 8 ɡeː 18 cop-ɡe 9 ɡuː 19 cy-ɡu 10 cu-tʰãm* 20 kʰe ciː*When it appears on its own, 'ten' is usually said cu-tʰãm 'a full ten'. In combinations it is simply cu. Factors of 20 are formed from kʰe
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Attic Numerals
ATTIC NUMERALS were used by the ancient Greeks , possibly from the 7th century BC. They were also known as HERODIANIC NUMERALS because they were first described in a 2nd-century manuscript by Herodian . They are also known as ACROPHONIC NUMERALS because the symbols derive from the first letters of the words that the symbols represent: five, ten, hundred, thousand and ten thousand. See Greek numerals
Greek numerals
and acrophony . DECIMAL SYMBOL GREEK NUMERAL IPA 1 Ι – – 5 Π πέντε 10 Δ δέκα 100 Η ἑκατόν 1000 Χ χίλιοι / χιλιάς 10000 Μ μύριονThe use of Η for 100 reflects the early date of this numbering system: Η (Eta ) in the early Attic alphabet represented the sound /h/. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked
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Aegean Numerals
AEGEAN NUMBERS was the numeral system used by the Minoan and Mycenaean civilizations. They are attested in several Aegean scripts ( Linear A , Linear B
Linear B
). They may have survived in the Cypro-Minoan script , where a single sign with "100" value is attested so far on a large clay tablet from Enkomi
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Babylonian Numerals
BABYLONIAN NUMERALS were written in cuneiform , using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. The Babylonians , who were famous for their astronomical observations and calculations (aided by their invention of the abacus ), used a sexagesimal (base-60) positional numeral system inherited from either the Sumerian or the Eblaite civilizations. Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units). CONTENTS * 1 Origin * 2 Characters * 3 Zero * 4 See also * 5 Notes * 6 Bibliography * 7 External links ORIGINThis system first appeared around 2000 BC; its structure reflects the decimal lexical numerals of Semitic languages
Semitic languages
rather than Sumerian lexical numbers
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Egyptian Numerals
The system of ancient EGYPTIAN NUMERALS was used in Ancient Egypt from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs . The Egyptians had no concept of a place-valued system such as the decimal system . The hieratic form of numerals stressed an exact finite series notation, ciphered one to one onto the Egyptian alphabet
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Etruscan Numerals
The ETRUSCAN NUMERALS were used by the ancient Etruscans . The system was adapted from the Greek Attic numerals and formed the inspiration for the later Roman numerals
Roman numerals
via the Old Italic script . ETRUSCAN ARABIC SYMBOL * OLD ITALIC θu 1 𐌠 maχ 5 𐌡 śar 10 𐌢 muvalχ 50 𐌣 ? 100 or C 𐌟There is very little surviving evidence of these numerals. Examples are known of the symbols for larger numbers, but it is unknown which symbol represents which number. Thanks to the numbers written out on the Tuscania
Tuscania
dice , there is agreement that zal, ci, huθ and śa are the numbers up to six (besides 1 and 5). The assignment depends on whether the numbers on opposite faces of Etruscan dice add up to seven, like nowadays. Some dice found did not show this proposed pattern
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Roman Numerals
The numeric system represented by ROMAN NUMERALS originated in ancient Rome
Rome
and remained the usual way of writing numbers throughout Europe
Europe
well into the Late Middle Ages
Late Middle Ages
. Numbers in this system are represented by combinations of letters from the Latin alphabet . Roman numerals, as used today, are based on seven symbols: SYMBOL I V X L C D M VALUE 1 5 10 50 100 500 1,000The use of Roman numerals
Roman numerals
continued long after the decline of the Roman Empire
Roman Empire
. From the 14th century on, Roman numerals
Roman numerals
began to be replaced in most contexts by the more convenient Hindu-Arabic numerals ; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day
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Hebrew Numerals
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
Greek numerals
in the late 2nd century BC. The current numeral system is also 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, ultimately derived from the Egyptian Hieratic numerals . The Greek system was adopted in Hellenistic Judaism
Hellenistic Judaism
and had been in use in Greece since about the 5th century BC. In this system, there is no notation for zero , and the numeric values for individual letters are added together
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Āryabhaṭa Numeration
The ĀRYABHAṭA NUMERATION is a system of numerals based on Sanskrit phonemes . It was introduced in the early 6th century in India by Āryabhaṭa , in the first chapter titled Gītika Padam of his Aryabhatiya . It attributes a numerical value to each syllable of the form consonant+vowel possible in Sanskrit phonology , from ka = 1 up to hau = 1018 . CONTENTS * 1 History * 2 Example * 3 Numeral table * 4 See also * 5 References HISTORYThe basis of this number system is mentioned in the second stanza of the first chapter of Aryabhatiya . The Varga (Group/Class) letters ka to ma are to be placed in the varga (square) places (1st, 100th, 10000th, etc.) and Avarga letters like ya, ra, la .. have to be placed in Avarga places (10th, 1000th, 100000th, etc.). The Varga letters kak to ma have value from 1, 2, 3 .. up to 25 and Avarga letters ya to ha have value 30, 40, 50.. up to 100
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Cyrillic Numerals
CYRILLIC NUMERALS are a numeral system derived from the Cyrillic script , developed in the First Bulgarian Empire
First Bulgarian Empire
in the late 10th century. It was used in the First Bulgarian Empire
First Bulgarian Empire
and by South and East Slavic peoples
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, too, 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
Cyrillic numerals
may still be found in books written in the Church Slavonic language
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Georgian Numerals
The GEORGIAN NUMERALS are the system of number names used in Georgian , a language spoken in the country of Georgia . The Georgian numerals from 30 to 99 are constructed using a base-20 system, similar to the scheme used in Basque , French for numbers 80 through 99, or the notion of the score in English. The symbols for numbers in modern Georgian texts are the same Arabic numerals used in English, except that the comma is used as the decimal separator , and digits in large numbers are divided into groups of three using spaces or periods (full stops). An older method for writing numerals exists in which most of letters of the Georgian alphabet (including some obsolete letters) are each assigned a numeric value
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Greek Numerals
GREEK NUMERALS, also known as IONIC, IONIAN, MILESIAN, or ALEXANDRIAN NUMERALS, are a system of writing numbers using the letters of the Greek alphabet . In modern Greece
Greece
, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals
Roman numerals
are still used elsewhere in the West. For ordinary cardinal numbers , however, Greece
Greece
uses Arabic numerals
Arabic numerals
. CONTENTS * 1 History * 2 Description * 3 Table * 4 Higher numbers * 5 Zero * 6 See also * 7 References * 8 External links HISTORYThe Minoan and Mycenaean civilizations ' Linear A and Linear B alphabets used a different system, called Aegean numerals
Aegean numerals
, which included specialized symbols for numbers: 𐄇 = 1, 𐄐 = 10, 𐄙 = 100, 𐄢 = 1000, and 𐄫 = 10000
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Inuit Numerals
Inuit , like other Eskimo languages (and Celtic and Mayan languages as well), uses a vigesimal counting system. Inuit counting has sub-bases at 5, 10, and 15. Arabic numerals
Arabic numerals
, consisting of 10 distinct digits (0-9) are not adequate to represent a base-20 system. Students from Kaktovik, Alaska , came up with the KAKTOVIK INUPIAQ NUMERALS, which has since gained wide use among Alaskan Iñupiaq , and is slowly gaining ground in other countries where dialects of the Inuit language are spoken. The numeral system has helped to revive counting in Inuit, which had been falling into disuse among Inuit speakers due to the prevalence of the base-10 system in schools. The picture below shows the numerals 1–19 and then 0. Twenty is written with a one and a zero, forty with a two and a zero, and four hundred with a one and two zeros
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Armenian Numerals
The system of ARMENIAN NUMERALS is a historic numeral system created using the majuscules (uppercase letters) of the Armenian alphabet
Armenian alphabet
. There was no notation for zero in the old system, and the numeric values for individual letters were added together. The principles behind this system are the same as for the Ancient Greek numerals
Greek numerals
and Hebrew numerals
Hebrew numerals
. In modern Armenia, the familiar Arabic numerals
Arabic numerals
are used. Armenian numerals
Armenian numerals
are used more or less like Roman numerals
Roman numerals
in modern English, e.g. Գարեգին Բ. means Garegin II and Գ. գլուխ means Chapter III (as a headline). Since not all browsers can render Unicode Armenian letters, the classical transliteration is given
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Radix
In mathematical numeral systems , the RADIX or BASE is the number of unique digits , including zero, used to represent numbers in a positional numeral system . For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as (x)y with x as the string of digits and y as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses ), as it is the most common way to express value . For example, (100)dec = 100 (in the decimal system) represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. CONTENTS * 1 Etymology * 2 In numeral systems * 3 See also * 4 References * 5 External links ETYMOLOGY Radix
Radix
is a Latin word for "root"
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