page_title: History of the Hindu–Arabic numeral system
section_title: Development in India
hierarchical_section_title: History of the Hindu–Arabic numeral system / Development in India
caption_attribution_description: English: Edicts of Ashoka numerals
context_page_description: The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205".
  Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described outside India in Al-Khwarizmi's On the Calculation with Hindu Numerals, and second Al-Kindi's four-volume work On the Use of the Indian Numerals. Today the name Hindu–Arabic numerals is usually used.
context_section_description: During the Vedic period (1500–500 BCE), motivated by geometric construction of the fire altars and astronomy, the use of a numerical system and of basic mathematical operations developed in northern India. Hindu cosmology required the mastery of very large numbers such as the kalpa (the lifetime of the universe) said to be 4,320,000,000 years and the "orbit of the heaven" said to be 18,712,069,200,000,000 yojanas. Numbers were expressed using  a "named place-value notation", using names for the powers of 10, like dasa, shatha, sahasra, ayuta, niyuta, prayuta, arbuda, nyarbuda, samudra, madhya, anta, parardha etc., the last of these being the name for a trillion (10¹²). For example, the number 26,432 was expressed as "2 ayuta, 6 sahasra, 4 shatha, 3 dasa, 2." In the Buddhist text Lalitavistara, the Buddha is said to have narrated a scheme of numbers up to 10⁵³.
  The form of numerals in Ashoka's inscriptions in the Brahmi script (middle of the third century BCE) involved separate signs for the numbers 1 to 9, 10 to 90, 100 and 1000. A multiple of 100 or 1000 was represented by a modification (or "enciphering") of the sign for the number using the sign for the multiplier number. Such enciphered numerals directly represented the named place-value numerals used verbally. They continued to be used in inscriptions until the end of the 9th century.
  In his seminal text of 499 CE, Aryabhata devised a novel positional number system, using Sanskrit consonants for small numbers and vowels for powers of 10. Using the system, numbers up to a billion could be expressed using short phrases, e. g., khyu-ghṛ representing the number 4,320,000. The system did not catch on because it produced quite unpronounceable phrases, but it might have driven home the principle of positional number system (called dasa-gunottara, exponents of 10) to later mathematicians. A more elegant katapayadi scheme was devised in later centuries representing a place-value system including zero.
caption: The first Brahmi numerals, ancestors of Hindu-Arabic numerals, used by Ashoka in his Edicts of Ashoka circa 250 BCE.
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