How did decimals come about and what is the origin of decimals?

China has used decimal notation since ancient times, and some practical units of measurement also use the decimal system, so it is easy to produce decimal fractions, that is, the concept of decimals. The first to put this concept into words was Liu Hui in the Wei and Jin dynasties.

In the process of calculating pi, he used 7 units, such as ruler, inch, minute, centimeter, millimeter, second, and sudden; Smaller units are no longer named, but collectively referred to as "decimals".

By the Song and Yuan dynasties, the concept of decimal had been further popularized and more clearly represented. Yang Hui's "Daily Algorithm" (1262) contains a mantra for the conversion of two catties: "One seek, the next six two five; Two seeks, abdicate one, two, five", that is, 1 16 = 0?

The words "spacer" and "abdication" here already have the meaning of indicating the position of the decimal point. Qin Jiushao bet the unit under the chips that represent the unit digits of the integer part, for example: —indicates that the inch is the world's earliest decimal notation.

Decimals are made up of integer parts, decimal parts, and decimal points. When measuring an object, it is often not an integer number that is obtained, and the ancients invented decimal numbers to supplement integers Decimals are a special form of decimal fractions. The denominator is ......The fraction can be expressed as a decimal.

All fractions can be expressed as decimals, except for infinite non-cyclic decimals. Irrational numbers are infinite non-cyclic decimals.

The meaning of fractions can be explained in terms of sub-segmentation and synthesis activities, when a whole (referring to the benchmark quantity) is divided equally, the quantity that gathers one of the parts is called the component, and the fraction is used to represent or record the component. For example, 2 5 refers to the fraction of an integer divided into quintiles and then gathered in two of them.

When the whole is divided into tenths, hundreds, thousands, ......At this time, another method of recording is used: decimal. For example, 1 10 is written as 100 is written as 1000 is written as 1000 is written as a result, etc. Among them

It is called a decimal point and is used to separate the integer part from the fractional part that cannot form an integer. If the integer is not 0, it is called a decimal number, and if it is 0, it is called a pure decimal. From this, it can be seen that the meaning of decimals is part of the meaning of fractions.

Origin of decimals:

The name of the decimal is Zhu Shijie, a digital scholar of the Yuan Dynasty in China in the thirteenth century AD.

Proposed. In the thirteenth century, the notation of a lower cell to represent a decimal number appeared in China. In the West, decimal appeared very late. It was not until the 16th century that the French mathematician Clavis first used the decimal point as a mark for the boundary between the integer part and the decimal part.

Decimals are a special form of representation of real numbers. All fractions can be expressed as decimals, and the dot in the decimal is called the decimal point, which is the dividing point between the integer part of a decimal and the decimal part. A decimal with an integer part of zero is called a pure decimal, and a decimal with an integer part that is not zero is called a decimal with a decimal.

Decimal properties: Add or remove any zero at the end of the decimal part, and the size of the decimal remains the same. For example:. Move the decimal point to the right (or left) by n digits respectively, and the value of the decimal will expand (or shrink) by a factor of the nth power of the base.

A simplest fraction can be reduced to a finite decimal number if and only if its denominator contains only prime factors.

2 or 5 or both. Similarly, a simplest fraction can be turned into a positive integer.

The finite decimal of the base is a subset of the base prime factor if and only if its denominator.

A decimal number or numbers that repeat in sequence from a certain digit of the decimal part is called a cyclic decimal. Cyclic decimal numbers are also rational numbers and can be formed as fractions.

The decimal part has an infinite number of digits, and the decimal of one number or several digits that does not repeat one after another is called an infinite non-cyclic decimals.

Infinite non-cyclic decimal numbers are irrational numbers and cannot be reduced to fractional form.

In production and life, when human beings measure and calculate, they often cannot get the results of integers, and decimals are generated according to actual needs.

China is the first country to adopt the decimal value system for counting. This kind of counting method has made our country in ancient times in a leading position in numerical calculation for a long time, and decimal is also the earliest invention and use in China, which has experienced a long development process.

The first to put this concept into words was Liu Hui in the Wei and Jin dynasties.

He's calculating pi.

In the process, 7 units such as ruler, inch, minute, centimeter, millimeter, second, and sudden are used; Smaller units are no longer named, but collectively referred to as "decimals".

After Liu Hui, some astronomers and mathematicians also adopted this scientific decimal counting method from different angles. Qin Jiushao, a mathematician of the Song Dynasty.

In the Nine Chapters of the Book of Numbers, not only is there a large number of decimal operations, but his notation of decimal numbers is also very advanced: the single digit of a calculated number is marked with relevant words, and the integer part is clearly distinguished from the decimal part. For example, in the calculation of the scroll of repentance wheel 6 "Huantian Sanji", the number "324,506 steps and two minutes and five centimeters" (steps) is obtained.

He also used it in volumes 12 and 13, such as pure decimals.

It can be seen that during the Song and Yuan dynasties, China not only pointed out the single digit of the number in the notation of decimals, distinguished the integer part and the decimal part, but also expressed it very clearly for pure decimals. Since China's ancient calculations have always been carried out by aligning numbers, the operation of decimal places is not a problem. Therefore, it can be said that the decimal in China has developed to the modern level in the Song and Yuan dynasties, and compared with now, it is just that the decimal point is not used.

Ancient India. of mathematicians have also used decimal fractions when the square does not get the whole root. After the twelfth century, European mathematicians began to use decimal fractions, but there was no systematic method and it was not common enough. By 1585, Belgium.

An engineer and scholar of Stevenn published a booklet of only 7 pages "On Decimals", which quietly introduced the meaning of decimals in detail, and promoted decimals to all arithmetic operations, thus making great contributions to the promotion and popularization of decimals. The decimal point first appeared in the writings of the German mathematician Kravis in 1593 and was gradually adopted in Europe. In the 18th century, the decimal point notation method was introduced to China and gradually adopted.

The use of decimal numbers began very early in China, and Liu Hui clearly recorded it in the "Nine Chapters of Arithmetic". This is 1,200 years before the first Iranian mathematician to systematically use decimal fractions, Al Qassi, and more than 1,300 years before the Dutch mathematician Steven's On Decimals. In the book "On Decimal", the theory of decimal numbers was explicitly expounded for the first time in Europe.

During the Yuan Dynasty in China, Liu Jin proposed the world's earliest decimal notation in the Book of Lü Chengshu, and he lowered the decimal part by one square to express it. Therefore, when people write decimals, if they write the decimal part, they will write the decimal part down one square, which is slightly smaller than the integer part. For example, if you want to write it, you should write it as a century, and the German mathematician Rudolf uses a vertical line to separate the integer part from the decimal part, for example, it is expressed as 257l36.

In the 17th century, the English mathematician Tempore used a comma "," as the dividing point between integer and decimal parts, e.g. 17,2. It is easy to confuse this with the comma in the text description, but at that time Liang Shou did not find a better way.

In the late 17th century, Indian mathematicians first used the small dot "·" when studying fractions. to separate the integer part from the decimal part, and it is only at this time that the decimal point is truly born.

In the 3rd century AD, that is, more than 1600 years ago, Liu Hui, a great mathematician in China, proposed decimals.

Originally, decimals were expressed as literal characters, and it was not until the 13th century that people used the lower squares, such as the one on the left for the whole part, and the lower right for the decimal part.

In ancient times, there were also people who remembered decimal numbers by enclosing the numbers of the decimal part in a circle, for example: 1, so that the circle separated the integer part from the decimal part. This notation later spread to Central Asia and Europe.

In 1427 A.D., the Central Asian mathematician Alcasi created a new method of notation of decimals, in which he used the method of separating the integer part from the decimal part, such as 3 14.

It was not until the 16th century that Europeans paid attention to the role of decimals. In Europe, there were people who kept decimal numbers like this, such as 3 1 4 1 5. It can be seen as a demarcation mark for the integer part, and the numbers in the circle indicate the order of the digits, which is interesting but troublesome.

It was not until 1592 A.D. that the Swiss mathematician Burke made great improvements to the representation of decimals, and he used a small circle to separate the integer part from the decimal part, for example: the small circle in the number actually plays the role of a decimal point.

After some time, the German mathematician Kravis replaced the small circles with small black dots. As a result, the way decimal is written has become our current representation.

However, in decimals, there are also different methods in different countries. Now, there are two ways to write the decimal point: one is to use", and the other is to use a small black dot”

It is commonly used in Germany, France and other countries", and "write decimal numbers such as , 51......, while the United Kingdom and some countries in Northern Europe drink the same as our country, with ". ." means a decimal point, such as.

The origin of decimals, do you know, after reading the knowledge.

The ancients accidentally dripped ink!

Decimals were first proposed and used in China. As early as more than 1,700 years ago, Liu Wei, an ancient mathematician in China, was born in the third century A.D., a native of Shandong, and a great mathematician in ancient China. The first person in the world to propose the concept of decimal decimals.

His masterpieces "Nine Chapters of Arithmetic Notes" and "Island Arithmetic" are the most valuable mathematical heritage of our country. In solving a mathematical puzzle, it was proposed that the part below the whole bit that cannot be named is called a micro.

Origin of decimals:

The earliest fraction is called a "single fraction", and it is a part of a unit that is divided into units as a whole. As early as 1700 B.C., the ancient Egyptians had a complete understanding of "single fractions" and could use several "single fractions" to represent other fractions with a numerator greater than 1.

Decimals, i.e. decimal fractions without denominator. There are two prerequisites for the generation of decimals: one is the use of decimal notation; The second is the refinement of the concept of fractions.

The advent of decimal marks the expansion of decimal notation from integers to fractions, making fractions and integers formally unified. China's understanding of decimal numbers is also the earliest in the world. In the 3rd century AD, the Chinese mathematician Liu Hui proposed decimal decimal numbers when dealing with the problem of square roots in the annotation "Nine Chapters of Arithmetic".

Isn't it complete? The only book is the division of different scales and units!

And that's how the change came.

Decimals were first proposed and used in China. As early as the third century A.D., our country was ancient.

Home Liu Wei is solving one.

It was proposed that the part below the entire bit that cannot be named is called a micro.

The name of the decimal socks shop was proposed by Zhu Shijie, a digital scholar of the Yuan Dynasty in China in the thirteenth century. In the thirteenth century, there was a notation of a lower cell to represent a decimal number in China, such as writing ||

In the West, decimal appeared very late. It was not until the 16th century that the French mathematics source Cravis first used the decimal point as a mark for the division between integer and decimal parts.