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Their symbols were based on the ancient counting rods.

It is a complicated question to determine exactly when the Chinese started calculating with positional representation, but it was definitely before 400 BC.

Their addition algorithm was identical to ours, and their multiplication algorithm was only very slightly different.

Their long division algorithm was the same, and the square root algorithm that was once taught in school was known to Archimedes, who may have invented it.

This allowed the system to consistently represent both large and small integers.

This approach eventually replaced all other systems.

The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory.

The prehistory of arithmetic is limited to a small number of artifacts which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed.

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Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals and the vigesimal (base 20) system that defined Maya numerals.

Since they also lacked a symbol for zero, they had one set of symbols for the unit's place, and a second set for the ten's place.

For the hundred's place they then reused the symbols for the unit's place, and so on.

The ancient Chinese were the first to meaningfully discover, understand, and apply negative numbers as explained in the Nine Chapters on the Mathematical Art (Jiuzhang Suanshu), which was written by Liu Hui.

The gradual development of Hindu–Arabic numerals independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing 0.