The ancients didn't learn numbers. How do they count?
As we all know, the ancient Babylonians used dots to represent numbers, with six dots representing "6" and eight dots representing "8" ... but what if there are more and more dots? They invented "
This symbol can represent both 60 and 360, which is easily confused. Moreover, there were two decimal systems in ancient Babylon, decimal system and sexagesimal, which brought inconvenience to the calculation.
The numbers of ancient Egyptians were "simple" and "hieroglyphics". Of course, it is much more complicated than the numbers we use now, such as:
When it means 654.38+00000, draw the shape of a person kneeling on his knees and raising his hands above his head.
This counting method is still in use. V stands for 5, X stands for 10, L stands for 50, C stands for 100, D stands for 500 and M stands for 1000.
The number is repeated several times, which is equivalent to several times this number. For example, XX stands for 20 and MMM stands for 3000. ...
Principle (left minus right plus): large numbers are reduced to the left and decimals are added to the right, which is similar to the translation law of numbers on the number axis.
What about the bigger number? They also stipulate to draw a horizontal line on the number, indicating that it is 1000 times, for example:
There is no need to explain too much about this. One, two, three, four ...
It appeared relatively late, but it has become an Arabic numeral widely used all over the world. Every number of 1~9 is marked with unnecessary symbols except for simple writing, so it will not be confused.
When we buy food in the vegetable market, if the price is 2.9 yuan, we usually say "two dollars and nine cents" instead of "three dollars and ten cents short." This statement is correct, but it doesn't conform to our daily habits, but it inspires us to improve the current counting method from another angle.
Of course, this is not the first thing people think of now. As early as1the first half of the 8th century (1726), this "addition and subtraction notation" was proposed.
This symbol does not need the numbers 6, 7, 8 and 9. For example, 6= 10-4, 7 = 10-3, 8 = 10-2, 9 =10-0/as follows:
The principle is to add a horizontal line to the number, which means subtraction.
Larger numbers are also acceptable, such as 489 = 500- 1 1, 3888 = 4000-12,2781(only 78), as follows.
What are the advantages of this counting method?
(1) without the four numbers of 6, 7, 8 and 9, it is easier to know large numbers and add and subtract;
Let's look at the following examples and feel the difference between traditional addition and new addition.
In the new addition, positive and negative cancellation can be used to speed up the calculation.
(2) subtraction and addition are the same thing, and all subtraction is converted into addition: for example
Subtraction becomes addition, as long as you can add.
(3) It is possible to learn our 99 multiplication table abroad. 99 The multiplication table has changed from the original 36 sentences (excluding 1) to the current 10 sentence:
2×2,2×3,2×4,2×5,3×3,3×4,3×5,4×4,4×5,5×5
(4) In the approximate calculation, there is no "rounding" now, instead, it is a simple and rude ending. For example: 3.0886, rounded, keeping the integer 3, accurate to one tenth: 3. 1, accurate to one percent: 3.09, accurate to one thousandth: 3.089.
In the new notation, the number of 3.0886 is:
Stay in the tenth place, 3. 1,
The question is, how does the new notation calculate multiplication and division?
Give a short answer example: 17×4=68.
You can try the branch yourself. Welcome to communicate.
Written at the end, but unfortunately, this algorithm can not be popularized, because the cost of change is too high. ...
What we are talking about today is just an armchair strategist ... don't take it too seriously.