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China

The Sūnzĭ Suànjīng, of unknown date but estimated to be dated from the 1st to 5th centuries AD, and Japanese records dated from the 18th century, describe how the 4th century BC Chinese counting rods system enabled one to perform decimal calculations. As noted in the Xiahou Yang Suanjing (425–468 AD), to multiply or divide a number by 10, 100, 1000, or 10000, all one needs to do, with rods on the counting board, is to move them forwards, or back, by 1, 2, 3, or 4 places. The rods gave the decimal representation of a number, with an empty space denoting zero. The counting rod system is a positional notation system.

Zero was not treated as a number at that time, but as a "vacant position". Qín Jiǔsháo 's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol 〇 for zero. The origin of this symbol is unknown; it may have been borrowed from Indian sources or produced by modifying a square symbol. Chinese authors had been familiar with the idea of negative numbers by the Han dynasty (2nd century AD), as seen in The Nine Chapters on the Mathematical Art.