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One may distinguish between the decimal system involved, also known as the Hindu-Arabic numeral system, and the precise glyphs used. The glyphs most commonly used in conjunction with the Latin alphabet since Early Modern times are 0 1 2 3 4 5 6 7 8 9.
The numbers were developed in India by the Hindus around 400 BCE. However, because it was Arabs who relayed this system to the West after the Hindu numerical system found its way to Baghdad, the numeral system became mis-identified as "Arabic" in the eyes of the Europeans. Arabs themselves call the Eastern Arabic numerals "Indian numerals," أرقام هندية, (arqam hindiyyah) and use a different set of Arabic symbols as numerals.
Main article: History of the Hindu-Arabic numeral system
The symbols for 1 to 9 in the Hindu-Arabic numeral system evolved from the Brahmi numerals. Buddhist inscriptions from around 300 BCE use the symbols which became 1, 4 and 6. One century later, their use of the symbols which became 2, 4, 6, 7 and 9 was recorded.
Use of the 0 glyph is first recorded in the 9th century, in an inscription at Gwalior dated to 870, and in the work of Al-Khwarizmi.
Brahmi numerals in India in the first century CE Modern day Arab telephone keypad with Hindu-Arabic numerals and corresponding Arabic-language numeralsThe numeral system came to be known to both the Persian mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals written about 825, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830, are principally responsible for the diffusion of the Indian system of numeration in the Middle-East and the West . In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952-953.
In the Arab World—until modern times—the Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used the Abjad numerals. Therefore, it was not until Fibonacci that the Arabic numeral system was used by a large population.
A distinctive "West Arabic" variant of the symbols begins to emerge in ca. the 10th century in the Maghreb and Al-Andalus, called the ghubar ("sand-table" or "dust-table") numerals.
The first mentions of the numerals in the West are found in the Codex Vigilanus of 976 . From the 980s, Gerbert of Aurillac (later, Pope Silvester II) began to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth, and he is known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.
Adoption in Europe
German manuscript page teaching use of Arabic numerals (Talhoffer Thott, 1459). At this time, knowledge of the numerals was still widely seen as esoteric, and Talhoffer teaches them together with the Hebrew alphabet and astrology. Woodcut showing the 16th century astronomical clock of Uppsala cathedral, with two clockfaces, one with Arabic and one with Roman numerals. Late 18th century French revolutionary "decimal" clockface.Al-Khwarizmi's 825 treatise On the Calculation with Hindu Numerals was translated into Latin in the 12th century, as Algoritmi de numero Indorum (Algoritmi being the translator's rendition of the author's name, al-ḫwārizmī, ultimately leading to the term algorithm).
Fibonacci, an Italian mathematician who had studied in Bejaia (Bougie), Algeria, promoted the Arabic numeral system in Europe with his book Liber Abaci, which was published in 1202, still describing the numerals as "Indian" rather than "Arabic".
"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 numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement was adopted identically into the numerals as used in Europe. The Latin alphabet running from left to right, unlike the Arabic alphabet, this resulted in an inverse arrangement of the place-values relative to the direction of reading.
The European acceptance of the numerals was accelerated by the invention of the printing press, and they became commonly known during the 15th century. The first known use in England was on a 1487 inscription (the date being written in Arabic numerals) at Piddletrenthide church, Dorset. By the mid 16th century, they were in common use in most of Europe. Roman numerals remained in use mostly for the notation of years of the Common Era, and for numbers on clockfaces. Sometimes, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical enumeration), and numbering pages in prefatory material in books.
Evolution of symbols
Main articles: Algorism and glyphs used with the Hindu-Arabic numeral system
The numeral system employed, known as Algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Arabic numeral system, all of which evolved from the Brahmi numerals. The symbols used to represent the system have split into various typographical variants since the Middle Ages:
the widespread Western "Arabic numerals" used with the Latin alphabet, in the table below labelled "European", descended from the "West Arabic numerals" which were developed in al-Andalus and the Maghreb (There are two typographic styles for rendering European numerals, known as lining figures and text figures).
the "Arabic-Indic" or "Eastern Arabic numerals" used with the Arabic alphabet, developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals used in Persian and Urdu languages as shown as "East Arabic-Indic".
the "Devanagari numerals" used with Devanagari and related variants grouped as Indian numerals.
The Arabic numerals are encoded in ASCII (and Unicode) at positions 48 to 57:
Binary Dec Hex Glyph
0011 0000 48 30 0
0011 0001 49 31 1
0011 0010 50 32 2
0011 0011 51 33 3
0011 0100 52 34 4
0011 0101 53 35 5
0011 0110 54 36 6
0011 0111 55 37 7
0011 1000 56 38 8
0011 1001 57 39 9