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{{Short description|Most common system for writing numbers}}

{{Numeral systems|expand=Place-value notation|expand2=Hindu-Arabic numeral system}}
[[File:EgyptphoneKeypad.jpg|upright=1.2|thumb|Modern-day Arab telephone keypad with two forms of Arabic numerals: Western Arabic numerals on the left and Eastern Arabic numerals on the right]]

The '''Hindu–Arabic numeral system''' or '''Indo-Arabic numeral system'''<ref name="booksmith">[[Audun Holme]], [https://books.google.com/books?id=zXwQGo8jyHUC&dq=%22indo+arabic+numeral+system%22&pg=PA188 Geometry: Our Cultural Heritage], 2000</ref> (also called the '''Hindu numeral system''' or '''Arabic numeral system''')<ref>{{cite book|url=https://books.google.com/books?id=uIgxAQAAIAAJ&q=%22empire+was+expanding+and+contact+was+made+with+India%22|title=Collier's Encyclopedia, with bibliography and index|author=William Darrach Halsey, Emanuel Friedman|year=1983|quote=When the Arabian empire was expanding and contact was made with India, the Hindu numeral system and the early algorithms were adopted by the Arabs}}</ref>{{refn|group=note|[[Hindustan|Hindu]] was the Persian name for "Indian" in the 10th century, when the Arabs adopted the number system. The use of "[[Hinduism|Hindu]]" to refer to a religion was a later development.}} is a [[positional notation|positional]] [[decimal]] [[numeral system]], and is the most common system for the symbolic representation of numbers in the world.

It was invented between the 1st and 4th centuries by [[Indian mathematics|Indian mathematicians]]. The system was adopted in [[Arabic mathematics]] by the 9th century. It became more widely known through the writings of the Persian mathematician [[Muhammad ibn Musa al-Khwarizmi|Al-Khwārizmī]]<ref name="Brezina2006">{{citation|last=Brezina|first=Corona|title=Al-Khwarizmi: The Inventor of Algebra|url=https://books.google.com/books?id=3Sfrxde0CXIC&pg=PA39|year=2006|publisher=The Rosen Publishing Group|isbn=978-1-4042-0513-0|pages=39–40}}: "Historians have speculated on al-Khwarizmi's native language. Since he was born in a former Persian province, he may have spoken the Persian language. It is also possible that he spoke Khwarezmian, a language of the region that is now extinct."</ref> (''On the Calculation with Hindu Numerals'', {{circa|825}}) and Arab mathematician [[Al-Kindi]] (''On the Use of the Hindu Numerals'', {{circa|830}}). The system had spread to medieval Europe by the [[High Middle Ages]].

The system is based upon ten (originally nine) [[glyph]]s. The symbols (glyphs) 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]]; and the Indian numerals in various scripts used in the [[Indian subcontinent]].

==Origins==
The Hindu{{ndash}}Arabic or Indo{{ndash}}Arabic numerals were invented by mathematicians in [[Indian subcontinent|India]].<ref>{{cite book |last1=Klein |first1=Felix |url=https://books.google.com/books?id=vfSutjEIZXkC&pg=PA6 |title=Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis |publisher=Cosimo, Inc. |year=2009 |isbn=978-1605209319 |pages=25,80 |via=Google Books}}</ref> Persian and Arabic mathematicians called them "Hindu numerals". Later they came to be called "Arabic numerals" in Europe because they were introduced to the West by Arab merchants.<ref name="UniOfNthC1">{{Citation|url=http://www.ibiblio.org/units/roman.html|title=Roman and "Arabic" Numerals|last=Rowlett|first=Russ|date=2004-07-04|publisher=[[University of North Carolina at Chapel Hill]]|access-date=2019-04-12}}</ref> According to various sources this number system has its origin in Chinese Shang numerals (1200 BC), which was also a decimal positional value system of base 10.<ref>{{Cite book |last1=Campbell |first1=Douglas M. |url=https://books.google.com/books?id=PFNsm_IaymYC&dq=shang+numerals+brahmi&pg=PA31 |title=Mathematics: People, Problems, Results |last2=Higgins |first2=John C. |date=1984 |publisher=Taylor & Francis |isbn=978-0-534-02879-4 |language=en}}</ref><ref>{{Cite journal |last=Lay-Yong |first=Lam |date=1988 |title=A Chinese Genesis: Rewriting the History of Our Numeral System |url=https://www.jstor.org/stable/41133830 |journal=Archive for History of Exact Sciences |volume=38 |issue=2 |pages=101–108 |issn=0003-9519}}</ref>

== Positional notation ==
{{main article|Positional notation|0 (number)}}

The Hindu–Arabic system is designed for [[positional notation]] in a [[decimal]] system. In a more developed form, positional notation also uses a [[Decimal separator|decimal marker]] (at first a mark over the ones digit but now more commonly a decimal point or a decimal comma which separates the ones place from the tenths place), and also a symbol for "these digits recur ''[[ad infinitum]]''". In modern usage, this latter symbol is usually a [[vinculum (symbol)|vinculum]] (a horizontal line placed over the repeating digits). In this more developed form, the numeral system can symbolize any [[rational number]] using only 13 symbols (the ten digits, decimal marker, vinculum, and a prepended [[minus sign]] to indicate a [[negative number]]).

Although generally found in text written with the Arabic [[abjad]] ("alphabet"), numbers written with these numerals also place the most-significant digit to the left, so they read from left to right (though digits are not always said in order from most to least significant<ref>In German, a number like 21 is said like "one and twenty", as though being read from right to left. In Biblical Hebrew, this is sometimes done even with larger numbers, as in Esther 1:1, which literally says, "Ahasuerus which reigned from India even unto Ethiopia, over seven and twenty and a hundred provinces".</ref>). The requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems.

== Symbols ==

Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, most of which developed from the [[Brahmi numeral]]s.

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 alphabet|Latin]], [[Cyrillic script|Cyrillic]], and [[Greek alphabet]]s in the table, descended from the "West Arabic numerals" which were developed in [[al-Andalus]] and the [[Maghreb]] (there are two [[Typography|typographic]] styles for rendering western Arabic numerals, known as lining figures and [[text figures]]).
* The "Arabic–Indic" or "[[Eastern Arabic numerals]]" used with Arabic script, developed primarily in what is now [[Iraq]].{{Citation needed|date=February 2020}} A variant of the Eastern Arabic numerals is used in Persian and Urdu.
* The [[Indian numerals]] in use with scripts of the [[Brahmic family]] in India and Southeast Asia. Each of the roughly dozen major scripts of India has its own numeral glyphs (as one will note when perusing Unicode character charts).

=== Glyph comparison ===

{| class="wikitable" style=text-align:center;
|- style=""
! colspan="10" | Symbol || Used with scripts || Numerals
|-
| 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || [[Arabic alphabet|Arabic]], [[Latin alphabet|Latin]], [[Cyrillic script|Cyrillic]], and [[Greek alphabet|Greek]] || [[Arabic numerals]]
|-
| {{Braille cell|#0}} || {{Braille cell|#1}} || {{Braille cell|#2}} || {{Braille cell|#3}} || {{Braille cell|#4}} || {{Braille cell|#5}} || {{Braille cell|#6}} || {{Braille cell|#7}} || {{Braille cell|#8}} || {{Braille cell|#9}} || [[Braille]]|| [[Braille#Derivation|Braille numerals]]
|-
| 𑁦 || 𑁧 || 𑁨 || 𑁩 || 𑁪 || 𑁫 || 𑁬 || 𑁭 || 𑁮 || 𑁯 || [[Brahmi script|Brahmi]] || [[Brahmi numerals]]
|-
| ० || १ || २ || ३ || ४ || ५ || ६ || ७ || ८ || ९ || [[Devanagari]] || [[Devanagari numerals]]
|-
| {{lang|ta|௦}} || {{lang|ta|௧}} || {{lang|ta|௨}} || {{lang|ta|௩}} || {{lang|ta|௪}} || {{lang|ta|௫}} || {{lang|ta|௬}} || {{lang|ta|௭}} || {{lang|ta|௮}} || {{lang|ta|௯}} || [[Tamil script|Tamil]] || [[Tamil numerals]]
|-
| ০ || ১ || ২ || ৩ || ৪ || ৫ || ৬ || ৭ || ৮ || ৯ || [[Bengali–Assamese script|Eastern Nagari]] || [[Bengali numerals]]
|-
| ੦ || ੧ || ੨ || ੩ || ੪ || ੫ || ੬ || ੭ || ੮ || ੯ || [[Gurmukhi]] || [[Gurmukhi numerals]]
|-
| ૦ || ૧ || ૨ || ૩ || ૪ || ૫ || ૬ || ૭ || ૮ || ૯ || [[Gujarati script|Gujarati]] || [[Gujarati numerals]]
|-
| 𑙐‎ || 𑙑 || 𑙒 || 𑙓‎ || 𑙔‎ || 𑙕 || 𑙖 || 𑙗 || 𑙘 || 𑙙 || [[Modi script|Modi]] || [[Modi script#Unicode|Modi numerals]]
|-
| ୦ || ୧ || ୨ || ୩ || ୪ || ୫ || ୬ || ୭ || ୮ || ୯ || [[Odia script|Odia]] || [[Odia numerals]]
|-
| ᱐ || ᱑ || ᱒ || ᱓ || ᱔ || ᱕ || ᱖ || ᱗ || ᱘ || ᱙ || [[Ol Chiki script|Santali]] || [[Ol Chiki script#Digits|Santali numerals]]
|-
| 𑇐 || 𑇑 || 𑇒 || 𑇓 || 𑇔 || 𑇕 || 𑇖 || 𑇗 || 𑇘 || 𑇙 || [[Sharada script|Sharada]] || [[Sharada script#Numerals|Sharada numerals]]
|-
| ౦ || ౧ || ౨ || ౩ || ౪ || ౫ || ౬ || ౭ || ౮ || ౯ || [[Telugu script|Telugu]] || {{slink|Telugu script|Numerals}}
|-
| ೦ || ೧ || ೨ || ೩ || ೪ || ೫ || ೬ || ೭ || ೮ || ೯ || [[Kannada script|Kannada]] || {{slink|Kannada script|Numerals}}
|-
| ൦ || ൧ || ൨ || ൩ || ൪ || ൫ || ൬ || ൭ || ൮ || ൯ || [[Malayalam script|Malayalam]] || [[Malayalam numerals]]
|-
|{{Script|Mtei|꯰}}
|{{Script|Mtei|꯱}}
|{{Script|Mtei|꯲}}
|{{Script|Mtei|꯳}}
|{{Script|Mtei|꯴}}
|{{Script|Mtei|꯵}}
|{{Script|Mtei|꯶}}
|{{Script|Mtei|꯷}}
|{{Script|Mtei|꯸}}
|{{Script|Mtei|꯹}}
|[[Meitei script]]
|{{slink|Meitei script|Numerals}}
|-
| ෦ || ෧ || ෨ || ෩ || ෪ || ෫ || ෬ || ෭ || ෮ || ෯ || [[Sinhala script|Sinhala]] || [[Sinhala numerals]]
|-
| 𑓐 || 𑓑‎ || 𑓒‎ || 𑓓‎ || 𑓔 || 𑓕‎ || 𑓖‎ || 𑓗 || 𑓘 || 𑓙‎ || [[Tirhuta script|Tirhuta Mithilakshar]] || [[Tirhuta script#Numerals|Maithili numerals]]
|-
| ༠ || ༡ || ༢ || ༣ || ༤ || ༥ || ༦ || ༧ || ༨ || ༩ || [[Tibetan script|Tibetan]] || [[Tibetan numerals]]
|-
| ၀ || ၁ || ၂ || ၃ || ၄ || ၅ || ၆ || ၇ || ၈ || ၉ || [[Burmese script|Burmese]] || [[Burmese numerals]]
|-
| ᠐ || ᠑ || ᠒ || ᠓ || ᠔ || ᠕ || ᠖ || ᠗ || ᠘ || ᠙ || [[Mongolian script|Mongolian]] || [[Mongolian numerals]]
|-
| ០ || ១ || ២ || ៣ || ៤ || ៥ || ៦ || ៧ || ៨ || ៩ || [[Khmer script|Khmer]] || [[Khmer numerals]]
|-
| ๐ || ๑ || ๒ || ๓ || ๔ || ๕ || ๖ || ๗ || ๘ || ๙ || [[Thai script|Thai]] || [[Thai numerals]]
|-
| ໐ || ໑ || ໒ || ໓ || ໔ || ໕ || ໖ || ໗ || ໘ || ໙ || [[Lao script|Lao]] || {{slink|Lao script|Numerals}}
|-
| ꧐ || ꧑ || ꧒ || ꧓ || ꧔ || ꧕ || ꧖ || ꧗ || ꧘ || ꧙ || [[Javanese script|Javanese]] || [[Javanese numerals]]
|-
| {{lang|ar|٠}} || {{lang|ar|١}} || {{lang|ar|٢}} || {{lang|ar|٣}} || {{lang|ar|٤}} || {{lang|ar|٥}} || {{lang|ar|٦}} || {{lang|ar|٧}} || {{lang|ar|٨}} || {{lang|ar|٩}} || [[Arabic]] || rowspan="3" | [[Eastern Arabic numerals]]
|-
| {{lang|fa|۰}} || {{lang|fa|۱}} || {{lang|fa|۲}} || {{lang|fa|۳}} || {{lang|fa|۴}} || {{lang|fa|۵}} || {{lang|fa|۶}} || {{lang|fa|۷}} || {{lang|fa|۸}} || {{lang|fa|۹}} || [[Persian alphabet|Persian]] / [[Dari]] / [[Pashto alphabet|Pashto]]
|-
| {{urd|{{lang|ur|۰}}}} || {{urd|{{lang|ur|۱}}}} || {{urd|{{lang|ur|۲}}}} || {{urd|{{lang|ur|۳}}}} || {{urd|{{lang|ur|۴}}}} || {{urd|{{lang|ur|۵}}}} || {{urd|{{lang|ur|۶}}}} || {{urd|{{lang|ur|۷}}}} || {{urd|{{lang|ur|۸}}}} || {{urd|{{lang|ur|۹}}}} || [[Urdu alphabet|Urdu]] / [[Shahmukhi]]
|-
| 〇/零 || 一 || 二 || 三 || 四 || 五 || 六 || 七 || 八 || 九 || [[East Asia]] || [[Chinese numerals|Chinese]], [[Vietnamese numerals|Vietnamese]], [[Japanese numerals|Japanese]], and [[Korean numerals]]
|-
| ο/ō || Αʹ || Βʹ || Γʹ|| Δʹ || Εʹ || Ϛʹ || Ζʹ || Ηʹ || Θʹ || [[Modern Greek]] || [[Greek numerals]]
|}

==History==
{{main article|History of the Hindu–Arabic numeral system}}

===Predecessors===
[[File:Edicts of Ashoka numerals.jpg|thumb|The first [[Brahmi numerals]], ancestors of Hindu-Arabic numerals, used by [[Ashoka]] in his [[Edicts of Ashoka]] {{circa|250 BC}}]]
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]].<ref>Flegg (2002), pp. 6ff.</ref>
[[File:Hindustani_numerals.svg|thumb|Nagari and Devanagari numerals with handwritten variants]]
[[Buddhist]] inscriptions from around 300 BC use the symbols that became 1, 4, and 6. One century later, their use of the symbols that became 2, 4, 6, 7, and 9 was recorded. These [[Brahmi numeral]]s are the ancestors of the Hindu–Arabic glyphs 1 to 9, but they were not used as a [[positional system]] with a [[0 (number)|zero]], and there were rather separate numerals for each of the tens (10, 20, 30, etc.).

The actual numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, and significantly younger than the Brahmi numerals.

===Development===
[[File:Evolution of Hindu-Arabic numerals.jpg|right|thumb|Development of Hindu–Arabic numerals]]
The place-value system is used in the [[Bakhshali manuscript]]; the earliest leaves being radiocarbon dated to the period 224–383 AD.<ref>
{{cite web|title=The Bakhshali manuscript|author=Pearce, Ian|publisher=The MacTutor History of Mathematics archive|url=http://www-history.mcs.st-andrews.ac.uk/HistTopics/Bakhshali_manuscript.html|date=May 2002|access-date=2007-07-24}}</ref> The development of the positional decimal system takes its origins in [[Indian mathematics]] during the [[Gupta period]]. Around 500, the astronomer [[Aryabhata]] uses the word ''kha'' ("emptiness") to mark "zero" in tabular arrangements of digits. The 7th century ''[[Brahmasphutasiddhanta|Brahmasphuta Siddhanta]]'' contains a comparatively advanced understanding of the mathematical role of [[0 (number)|zero]]. The Sanskrit translation of the lost 5th century Prakrit [[Jain cosmology|Jaina cosmological]] text ''[[Lokavibhaga]]''
may preserve an early instance of positional use of zero.<ref>Ifrah, G. The Universal History of Numbers: From prehistory to the invention of the computer. John Wiley and Sons Inc., 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk</ref>

These Indian developments were taken up in [[Islamic mathematics]] in the 8th century, as recorded in [[al-Qifti]]'s ''Chronology of the scholars'' (early 13th century).<ref>[[al-Qifti]]'s ''Chronology of the scholars'' (early 13th century):
: ''... a person from India presented himself before the [[Caliph]] [[al-Mansur]] in the year 776 who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ...''</ref>

The numeral system came to be known to both the [[Persian people|Persian]] mathematician [[Khwarizmi]], who wrote a book, ''On the Calculation with Hindu Numerals'' in about 825, and the [[Arab people|Arab]] mathematician [[Al-Kindi]], who wrote a book, ''On the Use of the Hindu Numerals'' ({{lang|ar|كتاب في استعمال العداد الهندي}} [''kitāb fī isti'māl al-'adād al-hindī'']) around 830. [[Persian people|Persian]] scientist [[Kushyar Gilani]] who wrote ''Kitab fi usul hisab al-hind ([[Principles of Hindu Reckoning]])'' is one of the oldest surviving manuscripts using the Hindu numerals.<ref>Martin Levey and Marvin Petruck, Principles of Hindu Reckoning, translation of Kushyar ibn Labban Kitab fi usul hisab al-hind, p. 3, University of Wisconsin Press, 1965</ref> These books are principally responsible for the diffusion of the Hindu system of numeration throughout the [[Islamic world]] and ultimately also to Europe.

The first dated and undisputed inscription showing the use of a symbol for zero appears on a stone inscription found at the [[Chaturbhuj Temple (Gwalior)|Chaturbhuja Temple]] at [[Gwalior]] in India, dated 876.<ref>{{cite web|url=https://www.ams.org/featurecolumn/archive/india-zero.html |title=All for Nought |work=Feature Column |author=Bill Casselman |author-link=Bill Casselman (mathematician) |publisher=AMS |date=February 2007}}</ref>

In 10th century [[Mathematics in medieval Islam|Islamic mathematics]], the system was extended to include [[fraction (mathematics)|fractions]], as recorded in a treatise by [[Abbasid Caliphate]] mathematician [[Abu'l-Hasan al-Uqlidisi]] in 952–953.<ref name=Berggrenn>{{cite book | first=J. Lennart | last=Berggren | title=The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook | chapter=Mathematics in Medieval Islam | publisher=Princeton University Press | year=2007 | isbn=978-0-691-11485-9 | page=518 }}</ref>

===Adoption in Europe===
{{main article|Arabic numerals}}
[[File:Codex Vigilanus Primeros Numeros Arabigos.jpg|thumb|right|The Arabic numeral system first appeared in Europe in the Spanish ''[[Codex Vigilanus]]'', year 976.]]

In Christian Europe, the first mention and representation of Hindu–Arabic numerals (from one to nine, without zero), is in the ''{{lang|la|[[Codex Vigilanus]]}}'' (aka ''Albeldensis''), an [[illuminated manuscript|illuminated]] compilation of various historical documents from the [[Visigoths|Visigothic]] period in [[Hispania|Spain]], written in the year 976 by three monks of the [[La Rioja (Spain)|Riojan]] monastery of [[San Martín de Albelda]].
Between 967 and 969, [[Pope Sylvester II|Gerbert of Aurillac]] discovered and studied Arab science in the Catalan abbeys. Later he obtained from these places the book ''{{lang|la|De multiplicatione et divisione}}'' (''On multiplication and division''). After becoming [[Pope Sylvester II]] in the year 999, he introduced a new model of [[abacus]], the so-called [[Pope Sylvester II#Abacus and Hindu–Arabic numerals|Abacus of Gerbert]], by adopting tokens representing Hindu–Arabic numerals, from one to nine.

[[Fibonacci|Leonardo Fibonacci]] brought this system to Europe. His book ''{{lang|la|[[Liber Abaci]]}}'' introduced [[Liber Abaci#Modus Indorum|Modus Indorum]] (the method of the Indians), today known as Hindu–Arabic numeral system or base-10 positional notation, the use of zero, and the decimal place system to the Latin world. The numeral system came to be called "Arabic" by the Europeans. It was used in European mathematics from the 12th century, and entered common use from the 15th century to replace [[Roman numerals]].<ref>{{cite web|url=http://www.halexandria.org/dward093.htm|title=Fibonacci Numbers|website=www.halexandria.org}}</ref><ref>H[https://www.britannica.com/eb/article-4153/Leonardo-Pisano Leonardo Pisano: "Contributions to number theory"]. [[Encyclopædia Britannica]] Online, 2006. p. 3. Retrieved 18 September 2006.</ref>

The familiar shape of the Western Arabic glyphs as now used with the Latin alphabet (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the product of the late 15th to early 16th century, when they entered early [[typesetting]].
Muslim scientists used the [[Babylonian numerals|Babylonian numeral system]], and merchants used the [[Abjad numerals]], a system similar to the [[Greek numerals|Greek numeral system]] and the [[Hebrew numerals|Hebrew numeral system]]. Similarly, Fibonacci's introduction of the system to Europe was restricted to learned circles.
The credit for first establishing widespread understanding and usage of the decimal positional notation among the general population goes to [[Adam Ries]], an author of the [[German Renaissance]], whose 1522 ''{{lang|de|Rechenung auff der linihen und federn}}'' (Calculating on the Lines and with a Quill) was targeted at the apprentices of businessmen and craftsmen.

<gallery>
File:Gregor Reisch, Margarita Philosophica, 1508 (1230x1615).png|{{lang|de|[[Gregor Reisch]]}}, ''{{lang|la|Madame Arithmatica}}'', 1508
File:Rechentisch.png|A {{Interlanguage link multi|calculation table|de|3=Rechnen auf Linien}}, used for arithmetic using [[Roman numerals]]
File:Rechnung auff der Linihen und Federn.JPG|{{lang|de|[[Adam Ries]]}}, ''{{lang|de|Rechenung auff der linihen und federn}}'', 1522
File:Köbel Böschenteyn 1514.jpg|Two arithmetic books published in 1514 – {{lang|de|Köbel}} (left) using a calculation table and {{lang|de|Böschenteyn}} using numerals
File:Rechnung auff der linihen 1525 Adam Ries.PNG|{{lang|de|[[Adam Ries]]}}, ''{{lang|de|Rechenung auff der linihen und federn}}'' (2nd Ed.), 1525
File:1543 Robert Recorde.PNG|[[Robert Recorde]], ''The ground of artes'', 1543
File:Peter Apian 1544.PNG|{{lang|de|[[Petrus Apianus|Peter Apian]]}}, ''{{lang|de|Kaufmanns Rechnung}}'', 1527
File:Adam riesen.jpg|{{lang|de|[[Adam Ries]]}}, ''{{lang|de|Rechenung auff der linihen und federn}}'' (2nd Ed.), 1525
</gallery>

=== Adoption in East Asia ===
In 690 AD, [[Wu Zetian|Empress Wu]] promulgated [[Chinese characters of Empress Wu|Zetian characters]], one of which was "〇". The word is now used as a synonym for the number zero.

In [[China]], [[Gautama Siddha]] introduced Hindu numerals with zero in 718, but [[Chinese mathematics|Chinese mathematicians]] did not find them useful, as they had already had the decimal positional [[counting rods]].<ref name="qian"/><ref>{{Citation
| title=Sangi o koeta otoko (The man who exceeded counting rods)
| last=Wáng
| first=Qīngxiáng
| isbn=4-88595-226-3
| publisher=Tōyō Shoten
| place=Tokyo
| year=1999
}}</ref>

In Chinese numerals, a circle (〇) is used to write zero in [[Suzhou numerals]]. Many historians think it was imported from [[Indian numerals]] by [[Gautama Siddha]] in 718, but some Chinese scholars think it was created from the Chinese text space filler "□".<ref name="qian">{{Citation
| title=Zhongguo Shuxue Shi (The history of Chinese mathematics)
| last=Qian
| first=Baocong
| year=1964
| publisher=Kexue Chubanshe
| place=Beijing
}}</ref>

Chinese and [[Japan]]ese finally adopted the Hindu–Arabic numerals in the 19th century, abandoning counting rods.

===Spread of the Western Arabic variant===
The "Western Arabic" numerals as they were in common use in Europe since the [[Baroque]] period have secondarily found worldwide use together with the [[Latin alphabet]], and even significantly beyond the contemporary [[spread of the Latin alphabet]], intruding into the writing systems in regions where other variants of the Hindu–Arabic numerals had been in use, but also in conjunction with [[Chinese script|Chinese]] and [[Japanese script|Japanese]] writing (see [[Chinese numerals]], [[Japanese numerals]]).

==See also==
*[[Arabic numerals]]
*[[Decimal]]
*[[History of mathematics]]
*[[Numeral system]]
*[[Positional notation]]
*[[0 (number)]]

==Notes==
{{Reflist|group=note}}

==References==
{{Reflist|30em}}

==Bibliography==
* Flegg, Graham (2002). ''Numbers: Their History and Meaning''. Courier Dover Publications. {{ISBN|0-486-42165-1}}.
* [http://www-history.mcs.st-and.ac.uk/HistTopics/Arabic_numerals.html The Arabic numeral system – MacTutor History of Mathematics]

==Further reading==
*Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. {{ISBN|0-262-13040-8}}.
*[http://digital.nls.uk/early-gaelic-book-collections/pageturner.cfm?id=77845307 On the genealogy of modern numerals] by Edward Clive Bayley

{{list of writing systems}}
{{Indian mathematics}}
{{Islamic mathematics}}

{{DEFAULTSORT:Hindu-Arabic Numeral System}}
[[Category:Numeral systems]]
[[Category:Numerals]]
[[Category:Elementary mathematics]]
[[Category:Indian inventions]]

Hindu–Arabic numeral system - Revision history

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