Fractional number

The first appearance of fractional numbers (fen shu in Chinese) was not a result of dividing two numbers. Fractions were considered as being whole numbers in themselves, and the word fen means to split or divide. Later, in the process of calculation, fractional numbers also appeared to denote the ratio of two whole numbers. Systematic fractional number algorithm appeared in the ancient math classic Jiuzhang Suanshu (Nine Chapters on Mathematical Art) in the Eastern Han Dynasty (25-220) around about the 1st century, which was about 1,400 years earlier than in Europe.

In the annotated version of Jiuzhang Suanshu by Liu Hui, it clearly shows the algorithm of the subtraction, addition, multiplication, and division of fractional numbers, which is identical to today's fractional calculations. Besides, other knowledge about fractions, including how to compare two fractions, and how to calculate the average of fractions, were also included in the book, making Jiuzhang Suanshu the earliest monograph that systematically discussed fractional numbers.

It is generally believed in Europe that the algorithm of fractional numbers originated in India, while the fact is the earliest Indian book on the algorithm of fractions appeared in the seventh century, in which introduced the same rules as the those in Jiuzhang Suanshu. And even the annotated version of Jiuzhang Suanshu by Liu Hui was completed in 263 in the Wei Dynasty (220-265), which means that the book is at least 400 years earlier than its counterpart in India.

  Decimal number

Also in the annotated version of Jiuzhang Suanshu by Liu Hui, the notion of the decimal number was first raised up. Liu invented the decimal number to denote the approximate number value of root extractions. Around the year 1300, Liu Jin in the Yuan Dynasty (1271-1368) wrote the number 106368.6312 as in his book Lvlv Chengshu. The notion of decimal number appeared in the West in 1585 and the expression is rather difficult. For instance, the same number mentioned above would be expressed as or 106368 .

Author: Jeff

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