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Arabic numerals are the ten symbols most commonly used to write decimal numbers: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 . They are also used for writing numbers in other systems such as octal, and for writing identifiers such as computer symbols, trademarks, or license plates. The term often implies a decimal number, in particular when contrasted with Roman numerals.
They are also called Western Arabic numerals, Ghubār numerals, Hindu-Arabic numerals,  Western digits, Latin digits, or European digits.  The Oxford English Dictionary differentiates them with the fully capitalized Arabic Numerals to refer to the Eastern digits.  The term numbers or numerals or digits often implies only these symbols, however this can only be inferred from context.
Europeans learned of Arabic numerals about the 10th century, though their spread was a gradual process. Two centuries later, in the Algerian city of Béjaïa, the Italian scholar Fibonacci first encountered the numerals; his work was crucial in making them known throughout Europe. European trade, books, and colonialism helped popularize the adoption of Arabic numerals around the world. The numerals have found worldwide use significantly beyond the contemporary spread of the Latin alphabet, and have become common in the writing systems where other numeral systems existed previously, such as Chinese and Japanese numerals.
Decimal notation was developed in India, with expansion to non-integers in Arabia. However this was done with different symbols.
The reason the digits are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic speakers of Spain and North Africa, who were then using the digits from Libya to Morocco. In the eastern part of the Arabian Peninsula, the Arabs were using the Eastern Arabic numerals or "Mashriki" numerals: ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩ [lower-alpha 1] 
Al-Nasawi wrote in the early 11th century that mathematicians had not agreed on the form of the numerals, but most of them had agreed to train themselves with the forms now known as Eastern Arabic numerals.  The oldest specimens of the written numerals available are from Egypt and date to 873–874 CE. They show three forms of the numeral "2" and two forms of the numeral "3", and these variations indicate the divergence between what later became known as the Eastern Arabic numerals and the Western Arabic numerals.  The Western Arabic numerals came to be used in the Maghreb and Al-Andalus from the 10th century onward.  Some amount of consistency in the Western Arabic numeral forms endured from the 10th century, found in a Latin manuscript of Isidore of Seville's Etymologiae from 976 and the Gerbertian abacus, into the 12th and 13th centuries, in early manuscripts of translations from the city of Toledo. 
Calculations were originally performed using a dust board (takht, Latin: tabula), which involved writing symbols with a stylus and erasing them. The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was called ḥisāb al-hindī in the east, it was called ḥisāb al-ghubār in the west (literally, "calculation with dust").  The numerals themselves were referred to in the west as ashkāl al‐ghubār ("dust figures") or qalam al-ghubår ("dust letters").  Al-Uqlidisi later invented a system of calculations with ink and paper "without board and erasing" (bi-ghayr takht wa-lā maḥw bal bi-dawāt wa-qirṭās). 
A popular myth claims that the symbols were designed to indicate their numeric value through the number of angles they contained, but no evidence exists of this, and the myth is difficult to reconcile with any digits past 4. 
The first mentions of the numerals from 1 to 9 in the West are found in the Codex Vigilanus of 976, an illuminated collection of various historical documents covering a period from antiquity to the 10th century in Hispania.  Other texts show that numbers from 1 to 9 were occasionally supplemented by a placeholder known as sipos, represented as a circle or wheel, reminiscent of the eventual symbol for zero. The Arabic term for zero is sifr (صفر), transliterated into Latin as cifra, and the origin of the English word cipher .
From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his position to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth. He was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France. 
The reception of Arabic numerals in the West was gradual and lukewarm, as other numeral systems circulated in addition to the older Roman numbers. As a discipline, the first to adopt Arabic numerals as part of their own writings were astronomers and astrologists, evidenced from manuscripts surviving from mid-12th-century Bavaria. Reinher of Paderborn (1140–1190) used the numerals in his calendrical tables to calculate the dates of Easter more easily in his text Compotus emendatus. 
Fibonacci, a mathematician from the Republic of Pisa who had studied in Béjaïa (Bugia), Algeria, promoted the Hindu-Arabic numeral system in Europe with his 1202 book Liber Abaci:
When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.
The Liber Abaci introduced the huge advantages of a positional numeric system, and was widely influential. As Fibonacci used the symbols from Béjaïa for the digits, these symbols were also introduced in the same instruction, ultimately leading to their widespread adoption. 
Fibonacci's introduction coincided with Europe's commercial revolution of the 12th and 13th centuries, centered in Italy. Positional notation could be used for quicker and more complex mathematical operations (such as currency conversion) than Roman and other numeric systems could. They could also handle larger numbers, did not require a separate reckoning tool, and allowed the user to check a calculation without repeating the entire procedure.  Although positional notation opened possibilities that were hampered by previous systems, late medieval Italian merchants did not stop using Roman numerals (or other reckoning tools). Rather, Arabic numerals became an additional tool that could be used alongside others. 
In the late 14th century only a few texts using Arabic numerals appeared outside of Italy. This suggests that the use of Arabic numerals in commercial practice, and the significant advantage they conferred, remained a virtual Italian monopoly until the late 15th century.  This may in part have been due to language – although Fibonacci's Liber Abaci was written in Latin, the Italian abacus traditions was predominantly written in Italian vernaculars that circulated in the private collections of abacus schools or individuals. It was likely difficult for non-Italian merchant bankers to access comprehensive information.
The European acceptance of the numerals was accelerated by the invention of the printing press, and they became widely known during the 15th century. Their use grew steadily in other centers of finance and trade such as Lyon.  Early evidence of their use in Britain includes: an equal hour horary quadrant from 1396,  in England, a 1445 inscription on the tower of Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a 1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription on the tomb of the first Earl of Huntly in Elgin Cathedral.  In central Europe, the King of Hungary Ladislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456. 
By the mid-16th century, they were in common use in most of Europe. Roman numerals remained in use mostly for the notation of Anno Domini (“A.D.”) years, and for numbers on clock faces.[ citation needed ] Other digits (such as Eastern Arabic) were virtually unknown.[ citation needed ]
Prior to the introduction of Arabic numerals, Cyrillic numerals, derived from the Cyrillic alphabet, were used by South and East Slavic peoples. The system was used in Russia as late as the early 18th century, although it was formally replaced in official use by Peter the Great in 1699.  Reasons for Peter's switch from the alphanumerical system are believed to go beyond his desire to imitate the West. Historian Peter Brown makes arguments for sociological, militaristic, and pedagogical reasons for the change. At a broad, societal level, Russian merchants, soldiers, and officials increasingly came into contact with counterparts from the West and became familiar with the communal use of Arabic numerals. Peter the Great also travelled incognito throughout Northern Europe from 1697 to 1698 during his Grand Embassy and was likely exposed to Western mathematics, if informally, during this time.  The Cyrillic numeric system was also inferior in terms of calculating properties of objects in motions, such as the trajectories and parabolic flight patterns of artillery. It was unable to keep pace with Arabic numerals in the growing science of ballistics, whereas Western mathematicians such as John Napier had been publishing on the topic since 1614. 
Chinese numeral systems that used positional notation (such as the counting rod system and Suzhou numerals) were in use in China prior to the introduction of Arabic numerals,   and some were introduced to medieval China by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.   
The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such as Morse code.
They are encoded in ASCII at positions 0x30 to 0x39. Masking to the lower four binary bits (or taking the last hexadecimal digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in Unicode.  EBCDIC used different values, but also had the lower 4 bits equal to the digit value.
|ASCII Binary||ASCII Octal||ASCII Decimal||ASCII Hex||Unicode||EBCDIC|
|0||0011 0000||060||48||30||U+0030 DIGIT ZERO||F0|
|1||0011 0001||061||49||31||U+0031 DIGIT ONE||F1|
|2||0011 0010||062||50||32||U+0032 DIGIT TWO||F2|
|3||0011 0011||063||51||33||U+0033 DIGIT THREE||F3|
|4||0011 0100||064||52||34||U+0034 DIGIT FOUR||F4|
|5||0011 0101||065||53||35||U+0035 DIGIT FIVE||F5|
|6||0011 0110||066||54||36||U+0036 DIGIT SIX||F6|
|7||0011 0111||067||55||37||U+0037 DIGIT SEVEN||F7|
|8||0011 1000||070||56||38||U+0038 DIGIT EIGHT||F8|
|9||0011 1001||071||57||39||U+0039 DIGIT NINE||F9|
|Symbol||Used with scripts||Numerals|
|౦||౧||౨||౩||౪||౫||౬||౭||౮||౯||Telugu||Telugu script § Numerals|
|೦||೧||೨||೩||೪||೫||೬||೭||೮||೯||Kannada||Kannada script § Numerals|
|໐||໑||໒||໓||໔||໕||໖||໗||໘||໙||Lao||Lao script § Numerals|
|٠||١||٢||٣||٤||٥||٦||٧||٨||٩||Arabic||Eastern Arabic numerals|
|۰||۱||۲||۳||۴||۵||۶||۷||۸||۹||Persian / Dari / Pashto|
|۰||۱||۲||۳||۴||۵||۶||۷||۸||۹||Urdu / Shahmukhi|
|〇||一||二||三||四||五||六||七||八||九||East Asia||Chinese numerals|
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today.
Fibonacci, also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano, was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".
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.
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents.
0 (zero) is a number representing an empty quantity. As a number, 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and other algebraic structures.
A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping.
Liber Abaci is a historic 1202 Latin manuscript on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci.
A numerical digit is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.
Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus.
Positional notation usually denotes the extension to any base of the Hindu–Arabic numeral system. More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred. In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string.
The Suzhou numerals, also known as Sūzhōu mǎzi (蘇州碼子), is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numerals are also known as huāmǎ (花碼), cǎomǎ (草碼), jīngzǐmǎ (菁仔碼), fānzǐmǎ (番仔碼) and shāngmǎ (商碼).
Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers. It is mathematically identical to the more commonly used long multiplication algorithm, but it breaks the process into smaller steps, which some practitioners find easier to use.
The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205".
The Hindu–Arabic numeral system or Indo-Arabic numeral system is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.
A numeral is a character that denotes a number. The decimal number digits 0–9 are used widely in various writing systems throughout the world, however the graphemes representing the decimal digits differ widely. Therefore Unicode includes 22 different sets of graphemes for the decimal digits, and also various decimal points, thousands separators, negative signs, etc. Unicode also includes several non-decimal numerals such as Aegean numerals, Roman numerals, counting rod numerals, Mayan numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Western Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, such as ² or ②, and composite characters such as ½.
A timeline of numerals and arithmetic
The Kaktovik numerals or Kaktovik Iñupiaq numerals are a base-20 system of numerical digits created by Alaskan Iñupiat. They are visually iconic, with shapes that indicate the number being represented.
Principles of Hindu Reckoning is a mathematics book written by the 10th- and 11th-century Persian mathematician Kushyar ibn Labban. It is the second-oldest book extant in Arabic about Hindu arithmetic using Hindu-Arabic numerals, preceded by Kibab al-Fusul fi al-Hisub al-Hindi by Abul al-Hassan Ahmad ibn Ibrahim al-Uglidis, written in 952.
An alphabetic numeral system is a type of numeral system. Developed in classical antiquity, it flourished during the early Middle Ages. In alphabetic numeral systems, numbers are written using the characters of an alphabet, syllabary, or another writing system. Unlike acrophonic numeral systems, where a numeral is represented by the first letter of the lexical name of the numeral, alphabetic numeral systems can arbitrarily assign letters to numerical values. Some systems, including the Arabic, Georgian and Hebrew systems, use an already established alphabetical order. Alphabetic numeral systems originated with Greek numerals around 600 BC and became largely extinct by the 16th century. After the development of positional numeral systems like Hindu–Arabic numerals, the use of alphabetic numeral systems dwindled to predominantly ordered lists, pagination, religious functions, and divinatory magic.