Algorism comprises all of the rules of performing arithmetic computations using a decimal system for representing numbers in which numbers written using ten symbols having the values 0 through 9 are combined using a place-value system (positional notation), where each symbol has ten times the weight of the one to its right. The decimal (base ten or occasionally denary) numeral system has ten as its base. ... A positional notation or place-value notation system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base or radix of that numeral system. ...

This system superseded earlier, more verbose, decimal systems where the symbols were different for each power of ten (and repeated instances gave the quantity of each power of ten) because at most ten symbols were needed for any range of numbers. The other systems needed a new symbol for every power of ten (and up to nine copies of each symbol for each of these).

Starting with the integer arithmetic developed in India using ten symbols in this way, Arabian mathematicians documented new arithmetic methods and made many other contributions to decimal arithmetic (including the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the decimal point). Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... The decimal separator is used to mark the boundary between the integer and the fractional parts of a decimal numeral. ...

The word algorism comes from the name al-Khwarizmi ("the one from Khwarizm") of an early 9th century Persian mathematician, possibly from what is now Khiva in western Uzbekistan. In English, it was first used about 1230 and then by Chaucer in 1391^[1]. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins thus: Soviet postage stamp commemorating the 1200th anniversary of Muhammad al‑Khwarizmi in 1983. ... Khiva (alternative names include Khorasam, Khoresm, Khwarezm, Khwarizm, Khwarazm, Chiwa and Chorezm) is a city in present day Uzbekistan, in the Province of Khorezm. ... As a means of recording the passage of time the 9th century was the century that lasted from 801 to 900. ... Khiva (alternative names include Khorasam, Khoresm, Khwarezm, Khwarizm, Khwarazm, Chiwa and Chorezm) is the former capital of Khwarezmia, which lies in the present-day Khorezm Province of Uzbekistan. ... Alexander of Villedieu[1] was a French author and a mathematician. ...

"Algorism is the art by which at present we use those Indian figures, which number two times five."

The word devolved into the modified form algorithm, with a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally algorism is also used in this generalized meaning, especially in older texts. In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ...

The place-value system

Algorism is based on the ten-symbol place value system, of which Georges Ifrah wrote^[2] George Ifrah (1947-) was a professor of mathematics, and a historian of mathematics, especially numerals. ...

See also

• Hindu-Arabic numeral system
• History of the Hindu-Arabic numeral system

I like cream cheese, it tastes good on toast. ... The Hindu-Arabic numeral system originaju from the Hindu numeral system, which is a pure place value system, that requires a zero. ...

References

1. ^ Oxford English Dictionary (first quote c1230CE, Chaucer c1391, and later quotes showing continuing usage since then)
2. ^ 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