This system was originally invented in India in the 6th century AD (or earlier), and was soon adopted in the Arab world. Arabian mathematicians made many contributions (including the concept of the decimal fractions as an extension of the notation), and the written European form of the digits is derived from the ghubar (sand-table or dust-table) numerals used in north-west Africa and Spain.
The word algorism comes from the Arabic al-Khwarizmi (“the one from Khwarizm”), the cognomen (nickname) of an early-9th-century mathematician, possibly from what is now Khiva in western Uzbekistan. (From whose name also comes the word algorithm.)