The decimal number is a number system based on 10. It consists of 10 basic numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.The decimal system, called Decimal System in English, is derived from the Greek Decem, meaning ten.Decimal counting was invented by Hindus 1500 years ago and passed down from Arabs to the 11th century.
In terms of computational mathematics, China had already had four operations in the Shang and Zhou Dynasties, and by the Spring and Autumn Period and the Warring States PeriodintegerThe four operations of and fraction are quite complete.Among them, the positive integer multiplication formula "Jiujiuge", which appeared in the Spring and Autumn Period, can be called an advanced decimalNumerationIt is the combination of concise Chinese language and characters, which can not be produced by any other notation and language and characters.Since then, "Jiujiu Song" has become one of the most basic foundations for the popularization and development of mathematics, and has continued to this day.
Use of decimal system
It is recorded in the Book of Prophecy that people in the Shang Dynasty had learned to record any number within 100000 in 13 words: one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand and ten thousand, but the largest number that can be confirmed at that time is 30000.oracular inscriptions on tortoise shells and bonesAndOdd number、even numbersandmultipleThe concept of.
DecimalPlace value notationIt includes two principles of decimal and bit value system, "decimal" means full decimal;The "bit value" is the samedigitThe values expressed in different positions are different, for example, the three digit "111", the "1" on the right represents one one in the single digit, the "1" in the middle represents one ten in the ten digit, and the "1" on the left represents one hundred in the hundred digit.This makes it extremely difficultintegerRepresentation and calculus have become so simple and easy that people tend to ignore its key role in the development of mathematics.
We have an idiom called“can be counted on one's fingers”It shows that ancient people could not count without their fingers, while ordinary people had just ten fingers.Therefore, the use of decimal system seems to be extremely natural.But the reality is not always the case.In the ancient civilization of Babylon, 60Carry system(This carry system still has traces today, such as one minute=60 seconds, etc.) In addition, there are also twenty carry systems.Ancient Egypt used the decimal system very early, but they did not know the place value system.The so-called bit value system is that what number a number represents depends on its location.The position value system is the crystallization of human wisdom for thousands of years.Zero isPlace value notationThe essence of.But its emergence is not easy.China is the first to use decimal systemNumerationAnd recognize the carry system.Our spoken or written numbers also follow this principle, such as 127.At the same time, we know 0 first.
The decimal system is an outstanding creation of the Chinese people and is of great significance in the history of world mathematics.Professor Joseph Needham, a famous British historian of science, once spoke highly of the numeration system of the Shang Dynasty in China. "If there were no such decimal system, it would be almost impossible for us to have a unified world". Joseph Needham said, "On the whole, the digital system of the Shang Dynasty was more advanced and scientific than that of Cuba and ancient Egypt at the same time."
Principles of use
The decimal system is based on the two principles of the decimal system and the decimal system, that is, all numbers are represented by 10 basic symbols, and the full decimal system is one. At the same time, the same symbol represents different values at different positions, so the position of the symbol is very important.The basic symbol is ten numbers from 0 to 9.To represent 10 times these ten numbers, move these numbers to the right by one digit and fill in the blanks with 0, that is, 10, 20, 30,90；To represent 10 times of these ten numbers, continue to move the number to the left, that is, 100200300.To represent 1/10 of a number, move the number to the right, and fill in the blanks with 0 if necessary: 1/10 bit 0.1, 1/100 is 0.01, and 1/1000 is 0.001.[1]
developing process
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Decimal in China
First of all, the decimal value system, which is indispensable in people's daily life, is a great invention of China.At the latestShang dynastyAt that time, China had adopted the decimal value system.Tao Wenhe of the Shang DynastyOracleIt can be seen that 13 numbers, including one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand and ten thousand, can be used to record any natural number within 100000.Although the shape of these numeration characters has changed in later generations and become the writing method of today, the numeration method has never been interrupted and has been followed and improved day by day.DecimalNumerationIt is the most advanced and scientific numeration method in the ancient worldWorld ScienceAnd the development of culture.As Joseph Needham said: "If there is no such tenCarry systemIt is impossible for us to have a unified world. "
Decimal is abroad
CubabironicNumerationAlthough it has the meaning of the bit value system, it uses the decimal system, and the calculation is very tedious.There were only two numbers from one to ten in ancient EgyptNumeric symbolThere are four numerical symbols from one hundred to ten million, and these symbols are pictographic, for example, a bird represents one hundred thousand.Because of its advanced geometry, ancient Greece despised calculation and its backward numeration method. It used all Greek letters to represent numbers ranging from one to ten thousand. If there were not enough letters, it would be supplemented by adding symbols such as "'".Ancient Rome used the cumulative method, such as ccc for 300.In ancient India, there were both letters and accumulation methods. The decimal value system was adopted in the seventh century AD, which was probably influenced by China.The current Indian Arabic numerals and numeration system were introduced to Europe around the tenth century.[2]
