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Origin of Fractions and Decimals
The score comes from the "point". A piece of land is divided into three parts, one of which is one third. One-third is a statement, which is written down with special symbols and becomes a score. The concept of score is formed by people's long-term experience in dealing with such problems.

The earliest music score in the world appeared on the papyrus scroll in Ammers, Egypt. In 1858, an Englishman named Henry Lint found an ancient papyrus in the ruins of Tiber, Egypt, and immediately restored this priceless treasure, and it took 19 years to translate the ancient Egyptian language on papyrus. Now this world's oldest math book is treasured in the British Museum in London.

In Ammers's grass scrolls, we saw the universal notation of fractions four thousand years ago, when the Egyptians had mastered the universal notation of single fractions-fractions with the numerator of 1. Egyptians believe that a fraction is the reciprocal of an integer. This understanding and the unified symbol of individual fractions are remarkable. It tells people that a number not only has an integer, but also its reciprocal-a single fraction.

But the score is not just a single score after all. In the 5th century BC, China began to realize that the quotient of dividing two integers is a fraction, which is the basis of the present concept of fraction. In this understanding, divisor also means fraction. In ancient China, the divisor was placed above the divisor, and the quotient remained above. For example, it is an incorrect score, which is different from the current symbol. The integer part with a fraction is placed above the fraction, not on the left. In the works of Arabs in the late12nd century, the numerator and denominator were first separated by a short horizontal line, which can be said to be the earliest fractional line in the world. /kloc-At the beginning of the third century, the Italian mathematician Fibonacci introduced Arabic mathematics into his works and introduced the notation of fractions into Europe.

Decimal, that is, decimal without denominator. There are two prerequisites for the generation of decimals: one is the use of decimal notation; The second is the promotion of the concept of scores. The appearance of decimal marks the extension of decimal notation from integer to fraction, which unifies the forms of fraction and integer. Our understanding of decimals is also the earliest in the world. In the 3rd century A.D., China mathematician Liu Hui put forward decimals when dealing with the square root problem in Notes on Nine Chapters of Arithmetic.

Although China's understanding of decimals was much earlier than that of Europe, the decimal notation used in modern mathematics was introduced to China from Europe.

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Origin of Fractions and Decimals

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Origin of decimals

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The difference between fractions and decimals

5/6 8/4 Teacher: We learned something about fractions and decimals respectively. In this lesson, we will learn the reciprocity of fractions and decimals together. (blackboard writing topic) 2. Carry out a new lesson 1? Teaching examples 1 examples given by multimedia courseware 1: 3/4, 1 1/25, 23/8 are all converted into decimals. Teacher: How to convert these scores into decimals? Compared with previous review, what knowledge do you think can be used to convert scores into decimals? To guide students to analyze, you can write the score as a division formula to calculate. Teacher: We can try to think about the relationship between fractions and division. How should I calculate it? After discussion, the students answer: You can rewrite the fraction into division and then find its fractional quotient. After the students fill in the form, ask the students how to fill it out and guide them to say: What information do you learn from the question? Students with ability can complete the thinking questions.

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The origin of decimal system.

In the 3rd century, that is, 1600 years ago, Liu Hui, a great mathematician in China, put forward decimals. At first, people only used words to represent decimals It was not until the13rd century that people used lower grids, such as 8.23 notation, where the left side represents the integer part and the lower right side represents the decimal part. In ancient times, some people memorized decimals by circling each number in the decimal part. For example, 1.5 is recorded as 1⑤, and this circle separates the integer part from the decimal part. This symbol was later spread to Central Asia and Europe. In A.D. 1427, Al Cassie, a mathematician in Central Asia, created a new decimal notation. He records decimals by separating integer parts from decimal parts, for example, 3. 14 is 3. 14. /kloc-in the 0 th and 6 th centuries, Europeans attached importance to the role of decimals. In Europe, some people recorded decimals like this at that time. For example, 3. 14 15 is 3 ⊙115 ⑤. ⊙ can be regarded as the boundary symbol of the integer part, and the numbers in the circle represent the order of the digits. This notation is interesting, but it is very troublesome. Until 1592, the Swiss mathematician Bhurki made great improvements in the representation of decimals. He uses a small circle to separate the integer part from the decimal part, such as 5. 24 ... The small circle in the number actually acts as a decimal point. After a while, German mathematician kravis replaced small circles with small black dots. So the writing of decimals has become our present representation. However, in different countries, the way of decimal representation is different. Now, there are two ways to write the decimal point: one is to use ","; One is to use small black dots. In German, French and other countries, ","is often used to write decimals, such as 3,42,7,565,438+0 ..., while some countries in Britain and Northern Europe, such as China, use "..." to represent decimal points, such as 65,438+0.3,4.5 ... The decimal point refers to the origin of decimals, that is, without denominator. There are two prerequisites for the generation of decimals: one is the use of decimal notation; The second is the promotion of the concept of scores. The appearance of decimal marks the extension of decimal notation from integer to fraction, which unifies the forms of fraction and integer. Our understanding of decimals is also the earliest in the world. In the 3rd century A.D., China mathematician Liu Hui put forward decimals when dealing with the square root problem in Notes on Nine Chapters of Arithmetic. Although China's understanding of decimals was much earlier than that of Europe, the decimal notation used in modern mathematics was introduced to China from Europe. Europe's greatest contribution to decimals is the Dutch engineer simon stevin (1548? 1620)。 He realized the advantages of decimals from making interest tables, so he strongly advocated introducing decimals into the whole arithmetic operation so that decimals could participate in counting effectively. But Steven's decimal notation is not brilliant, such as 139.654. He wrote 135 ⊙ 6 15243, and the number in the circle behind each number is used to indicate the position of the previous number. This representation complicates the form of decimals and brings great trouble to the operation of decimals. 1592, the Swiss mathematician Bhurki made great improvements. He used a small hollow circle to separate the integer part from the decimal part, for example, expressing 36.548 as 36. 548, which is very close to the modern performance. About a year later, in kravis, people used black dots instead of small circles for the first time. He made this practice known to the world in Algebra published in 1608, and the modern decimal notation was established. Hope to adopt. . . .

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Origin of natural numbers, negative numbers, fractions and decimals.

Humans are the product of animal evolution, and there was no concept of quantity at first. However, the developed brain's understanding of the objective world has reached a more rational and abstract level. In this way, in the long life practice, out of the need to record and distribute daily necessities, the concept of number has gradually emerged. For example, a wild animal is captured, which is represented by 1 stone. If you catch three heads, put three stones. "Knotting notes" is also something that many ancient humans on earth who are very close to each other do together. There is a record of "tying the knot to govern the country" in the book of changes. Legend has it that the ancient Persian kings tied knots with ropes to count the days of war. It is also a common method used by the ancients to carve or hide the bark with sharp tools or count it on the ground with small sticks. When these methods are used much more, the concept of number and the symbol of counting are gradually formed. At first, the concept of numbers began with natural numbers, such as 1, 2, 3, 4 ... No matter where they are located, the symbols used for counting are the same size. The figures in ancient Rome were quite advanced, and now many old wall clocks are often used. In fact, Roman numerals have only seven symbols: I (for 1), V (for 5), X (for 10), L (for 50), C (for 100), D (for 500) and M (for/kloc-). When they are combined according to the following rules, they can represent any number: 1 Number of repetitions: A Roman numeral symbol is repeated several times, indicating several times of this number. For example, "three" means "3"; "XXX" means "30" 2. Add right and subtract left: add a symbol representing big numbers to the right of the symbol representing small numbers, indicating that big numbers are added with small numbers, such as "VI" for "6" and "DC" for "600". A symbol representing a small number is attached to the left of the symbol representing a large number, indicating a number in which a large number is subtracted from a small number, such as "IV" for "4", "XL" for "40" and "VD" for "495". 3. Add a horizontal line: add a horizontal line to the Roman numeral, indicating that it is 1000 times that number. For example, ""means "15000" and "165000". In ancient China, notation was also very important. The oldest notation is found in Oracle Bone Inscriptions and Zhong Ding, but it is difficult to write and identify, so it is not used by future generations. In the Spring and Autumn Period and the Warring States Period, production developed rapidly. In order to meet this need, our ancestors created a very important calculation method-calculation. The computing chip used for calculation is made of bamboo sticks and bones. Arranged according to the specified length order, which can be used for counting and calculation. With the popularization of calculation, the arrangement of calculation and preparation has become the symbol of calculation. There are two types of calculation and arrangement, horizontal and vertical, both of which can represent the same number. It is clear from the absence of "10" in the calculation code that the calculation strictly follows the decimal system from the beginning. Numbers exceeding 9 digits will enter one digit. The same number, a hundred in a hundred, Wan Li has ten thousand. This calculation method was very advanced at that time. Because the decimal system was really used in other parts of the world at the end of the 6th century. But there is no "zero" in digital calculation, and there is a vacancy when it meets "zero". For example, "6708" can be expressed as "┴ ╥". There is no "zero" in the number, so it is easy to make mistakes. So later, some people put copper coins in the blank to avoid mistakes, which may be related to the emergence of "zero" However, most people believe that the invention of the mathematical symbol "0" should be attributed to Indians in the 6th century. They first used a black dot () to represent zero, and then gradually became "0". Speaking of the appearance of "zero", it should be pointed out that the word "zero" appeared very early in ancient Chinese characters. But at that time, it didn't mean "nothing", just "bits and pieces" and "not much". Such as "odd", "sporadic" and "odd". "105" means that there is a score of 100. With the introduction of Arabic numerals. "105" is pronounced as "105", and the word "zero" corresponds to "0", so "zero" means "0". If you look closely, you will find that there is no "0" in Roman numerals. In fact, in the 5th century, "0" was introduced to Rome. But the Pope is cruel and old-fashioned. He doesn't allow anyone to use "0". A Roman scholar recorded some benefits and explanations about the usage of "0" in his notes, so he was summoned by the Pope and executed the punishment of "Zn" so that he could no longer hold a pen and write. But no one can stop the appearance of "0". Now, "0" has become the most meaningful digital symbol. "0" can mean "No" or "Yes". For example, a temperature of 0℃ does not mean that there is no temperature; "0" is the only neutral number between positive and negative numbers; The power of 0 of any number (except 0) is equal to1; 0! = 1 (factorial of zero is equal to 1). In addition to decimal system, in the early stage of the germination of mathematics, there were many numerical decimal systems, such as five, binary, ternary, seven, eight, decimal, hexadecimal, twenty, hexadecimal and so on. In the long-term practical application, decimal has finally gained the upper hand. At present, the internationally used numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 are called Arabic numerals. In fact, they were first used by ancient Indians. Later, Arabs integrated ancient Greek mathematics into their own mathematics, and this simple and easy-to-remember decimal notation spread all over Europe, gradually evolving into today's Arabic numerals. The concept of numbers, the writing of numbers and the formation of decimal system are all the results of human long-term practical activities. With the needs of production and life, people find that it is not enough to express it only by natural numbers. If five people share four things when distributing prey, how much should each person get? So the score is generated. China's academic score is earlier than that of Europe 1400 years! Natural numbers, fractions and zeros are usually called arithmetic numbers. Natural numbers are also called positive integers. With the development of society, people find that many quantities have opposite meanings, such as increase and decrease, advance and retreat, rise and fall, east and west. To represent such a quantity, a negative number is generated. Positive integers, negative integers and zero are collectively called integers. If you add a positive score and a negative score, they are collectively called rational numbers. With these digital representations, people find it much more convenient to calculate. However, in the process of digital development, an unpleasant thing happened. Let's go back to Greece 2500 years ago, where there was a Pythagorean school, a group that studied mathematics, science and philosophy. They believe that "number" is the origin of all things and dominates the whole nature and human society. So everything in the world can be summed up as a number or a ratio of numbers, which is the source of world harmony. When they say numbers, they mean integers. The appearance of scores makes "number" different.