Although the shapes of these numbers have changed in later generations and become the current writing methods, the notation has never been interrupted and has been used and improved day by day.
Decimal notation is the most advanced and scientific notation in the ancient world, which plays an inestimable role in the development of world science and culture. As Joseph Needham said, "Without this decimal system, it is impossible to have our unified world now."
In computational mathematics, China had four operations in the Shang and Zhou Dynasties, and the four operations of integers and fractions in the Spring and Autumn Period and the Warring States Period were quite complete.
Among them, the positive integer multiplication formula "Jiujiuge" appeared in the Spring and Autumn Period, which can be called the crystallization of the combination of advanced decimal notation and concise China language, which can not be produced by any other notation and language.
Since then, Jiujiu Song has become one of the most basic foundations for the popularization and development of mathematics, and it has continued to this day. It only changed from "998 1" to "224" in ancient times, and now it is from "one for one" to "998 1".
Extended data:
I. Introduction to the decimal system:
600, 3/5,-7.99 ... Looking at these familiar numbers, do you think too much? In fact, this is the universal decimal system, which is 1. All decimal one, all decimal two, and so on ... 2. Expand by weight, the first weight is 10 0, the second weight is1kloc-0/... and so on, the nth bit is 65438+.
Second, the transformation:
Decimal numbers are converted into binary numbers.
When decimal number is converted into binary number, the integer part and decimal part of decimal number are converted separately and then merged because of the different conversion methods between integer number and decimal number.
1, the decimal integer is converted into a binary integer, and the decimal integer is converted into a binary integer by the method of "dividing by 2 to get the remainder, and arranging in reverse order". Specifically, divide the decimal integer by 2 to get a quotient and a remainder.
If you divide the quotient by 2, you will get a quotient and a remainder, and so on until the quotient is zero. Then the remainder obtained first is used as the low-order significant bit of the binary number, and the remainder obtained later is used as the high-order significant bit of the binary number, which are arranged in turn.
2. Decimal decimals are converted into binary decimals
The method of converting decimal fraction into binary fraction is "rounding by 2, in order". The specific method is: multiply the decimal part by 2 to get the product, take out the integer part of the product, multiply the remaining decimal part by 2 to get another product, then take out the integer part of the product, and so on until the decimal part in the product is zero or reaches the required accuracy.
Then, the extracted integer parts are arranged in sequence, with the first integer as the high-order significant bit of binary decimal and the last integer as the low-order significant bit.
References:
Baidu encyclopedia-decimal system