History of Chinese Invention - The Decimal System of Number Representations

The Decimal number system is also called HINDU-ARABIC, or ARABIC, or base 10 system. Mathematics commonly uses a positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and a dot (decimal point).

An example of how the Chinese used the decimal system may be seen in an inscription from the thirteenth century BC, in which '547 days' is written 'Five hundred plus four decades plus seven of days'. The Chinese wrote with characters instead of an alphabet. When writing with a Western alphabet of more than nine letters, there is a temptation to go on with words like eleven. Less elegant number schemes such as Roman numerals, built on positions by adding a unit to a power of ten symbol, without using placeholders (zeros). Eleven was X (ten) followed by I (one). This became even more unwieldy with or half powers of ten such as L for 50 or D for 50. With Chinese characters, ten is ten-blank and eleven is ten-one (zero was left as a blank space: 405 is 'four blank five'). A noteworthy characteristic of the Chinese system, and one that represented a substantial advantage over the Mediterranean systems, was its predilection for a decimal notation. This is demonstrated by early measuring rulers dating back as far as the 6th century BC.

This place holding or place notation was much easier than inventing a new character for each number (imagine having to memorize an enormous number of characters just to read the date!). Having a decimal system from the beginning was a big advantage in making mathematical advances. Most historians agree that the development of a decimal place value system of numeration originated from the Indian subcontinent, and that Arabic scholars were responsible for the system.

Some have argued the first use of a place value system should be attributed to the ancient Sumerians during the Proliterate period (3100-2800 BC). While it cannot be denied that the Babylonians used a place value system, theirs was sexagismal (base 60), and while the concept of place value may have come from Mesopotamia, the Indians were the first to use it with a decimal base (base 10). All current evidence points towards the Indian system having been influenced by the base 10 Chinese counting boards (precursor to the abacus) and the place value system of the Babylonians. Without doubt the use of a decimal base originates from the most basic human instinct of counting on one's fingers. The key contribution of the Indians however is not in the development of nine symbols to represent the numbers one to nine, but the invention of the place holder zero.

It is uncertain how much longer it took for zero to be invented but there is little doubt that such a symbol was in existence by 500 BC, if not in widespread use. The first evidence of decimals in Europe is in a Spanish manuscript of 976 AD by Gerbert, who had studied under Arabic mathematicians.

References

The Genius of China
3,000 Years of Science, Discovery and Invention
written by Robert K.G. Temple and published by Simon and Schuster, 1986
Currently out-of-print

Encyclopedia Brittanica, 2004

History of Ancient Sumeria
http://ufo.whipnet.org/creation/ancient.sumeria/