Numeral systems by culture  

HinduArabic numerals  
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Alphabetic numerals  
Abjad Armenian Āryabhaṭa Cyrillic 
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Other systems  
Attic Babylonian Brahmi Egyptian Etruscan Inuit 
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List of numeral system topics  
Positional systems by base  
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The HinduArabic numeral system is a decimal placevalue numeral system. It requires a zero to handle the empty powers of ten (as in "205").^{[1]}
Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th century, and is first described in AlKhwarizmi's On the Calculation with Hindu Numerals (ca. 825), and AlKindi's four volume work On the Use of the Indian Numerals (ca. 830)^{[2]}. Today the name HinduArabic numerals is usually used.
Evidence of early use of a zero glyph may be present in Bakhshali manuscript, a text of uncertain date, possibly a copy of a text composed as early as the 3rd century.
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Historians trace modern numerals in most languages to the Brahmi numerals, which were in use around the middle of the third century BC.^{[3]} The place value system, however, evolved later. The Brahmi numerals have been found in inscriptions in caves and on coins in regions near Pune, Mumbai, and Uttar Pradesh. These numerals (with slight variations) were in use over quite a long time span up to the 4th century AD^{[3]}.
During the Gupta period (early 4th century AD to the late 6th century AD), the Gupta numerals developed from the Brahmi numerals and were spread over large areas by the Gupta empire as they conquered territory ^{[3]}. Beginning around 7th century, the Gupta numerals evolved into the Nagari numerals.
There is indirect evidence that the Indians developed a positional number system as early as the first century CE^{[3]}. The Bakhshali manuscript (c. 3d c. BCE) uses a place value system with a dot to denote the zero, which is called shunyasthAna, "emptyplace", and the same symbol is also used in algebraic expressions for the unknown (as in the canonical x in modern algebra). However, the date of the Bakhshali manuscript is hard to establish, and has been the subject of considerable debate. The oldest dated Indian document showing use of the modern place value form is a legal document dated 346 in the Chhedi calendar, which translates to 594 CE^{[3]}. While some historians have claimed that the date on this document was a later forgery, it is not clear what might have motivated it, and it is generally accepted that enumeration using the placevalue system was in common use in India by the end of the 6th century. ^{[4]}. Indian books dated to this period are able to denote numbers in the hundred thousands using a place value system. ^{[5]} Many other inscriptions have been found which are dated and make use of the placevalue system for either the date or some other numbers within the text ^{[3]}, although some historians claim these to also be forgeries.
In his seminal text of 499, Aryabhata devised a positional number system without a zero digit. He used the word "kha" for the zero position.^{[3]}. Evidence suggests that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. [1]. The same documents sometimes also used a dot to denote an unknown where we might use x. Later Indian mathematicians had names for zero in positional numbers yet had no symbol for it.
The use of zero in these positional systems are the final step to the system of numerals we are familiar with today. The first inscription showing the use of zero which is dated and is not disputed by any historian is the inscription at Gwalior dated 933 in the Vikrama calendar (876 CE.) ^{[3]}^{[6]}.
The oldest known text to use zero is the Jain text from India entitled the Lokavibhaga , dated 458 AD.^{[7]}
The first indubitable appearance of a symbol for zero appears in 876 in India on a stone tablet in Gwalior. Documents on copper plates, with the same small o in them, dated back as far as the sixth century AD, abound.^{[8]}
Before the rise of the Arab Empire, the HinduArabic numeral system was already moving West and was mentioned in Syria in 662 AD by the Nestorian scholar Severus Sebokht who wrote the following:
According to alQifti's chronology of the scholars[3]:
The work was most likely to have been Brahmagupta's Brahmasphutasiddhanta (Ifrah) [4] (The Opening of the Universe) which was written in 628[5]. Irrespective of whether Ifrah is right, since all Indian texts after Aryabhata's Aryabhatiya used the Indian number system, certainly from this time the Arabs had a translation of a text written in the Indian number system. [6]
In his text The Arithmetic of AlUqlîdisî (Dordrecht: D. Reidel, 1978), A.S. Saidan's studies were unable to answer in full how the numerals reached the Arab world:
AlUqlidisi developed a notation to represent decimal fractions.^{[9]}^{[10]} The numerals came to fame due to their use in the pivotal work of the Persian mathematician AlKhwarizmi, whose book On the Calculation with Hindu Numerals was written about 825, and the Arab mathematician AlKindi, who wrote four volumes (see [2]) "On the Use of the Indian Numerals" (Ketab fi Isti'mal al'Adad alHindi) about 830. They, amongst other works, contributed to the diffusion of the Indian system of numeration in the MiddleEast and the West.
The evolution of the numerals in early Europe is shown below: The French scholar J.E. Montucla created this table “Histoire de la Mathematique”, published in 1757:











In the last few centuries, the European variety of Arabic numbers was spread around the world and gradually became the most commonly used numeral system in the world.
Even in many countries in languages which have their own numeral systems, the European Arabic numerals are widely used in commerce and mathematics.
The significance of the development of the positional number system is probably best described by the French mathematician Pierre Simon Laplace (1749  1827) who wrote:
Tobias Dantzig, the father of George Dantzig, had this to say in Number:
