Decimal system

Introduction to the decimal system

In the western world,Decimal number systemAlmost everyone knows the number.

Everyone knows.

Posted byjustI know.

There are many other number systems, but society has decided to use the decimal number system as the default number system.

why? I think the reason is that people use two hands (two feet) and five fingers, and it is natural to count from 1 to 10.

When you reach 10, you will reach 20 from zero.

That is my guess, a very reliable guess.

The decimal number system was invented by the Indians and popularized by the Arabs, and is still calledIndo-Arabic Numeral System.

It is said that the decimal number system hasbase 10Because it uses10 digits, From 0 to 9.

Numbers are positional, which means that numbers have different weights (values) depending on the position.

This1Numbers in numbers10Has a different value from the number31,because10It's in place2with31It's in place1(Counting from the right).

Although this sounds obvious because you have used this system since you were a kid, not every digital system can work this way.

From ancient Rome to the late Middle Ages, the Roman numeral system widely used in Europe is still "level 10", but not a position. representative10You used this letterX,representative100You usedC,representative1000You usedM.

In Roman numerals, the number243It can be expressed in the decimal number system asCCXLIII.

You cannot move the letters to change their meaning. Compared with letters of lower value, letters of higher value always move to the left. Relative to each letter, forming4useIV, For example (but this is another topic, let's go back to decimal numbers).

Any number in the decimal number system can be decomposed into the sum of other numbers and multiplied by a power of 10, depending on their location. Start at position 0 on the right.

\ [10 ^ 0 \] is equal to 1.

\ [10 ^ 1 \] is equal to 10.

\ [10 ^ 2 \] is equal to 100, and so on.

In the decimal number system:

5Can be expressed as \ [5 \ times10 ^ 0 \]

42Can be expressed as \ [4 \ times10 ^ 1 + 2 \ times10 ^ 0 \]

254It can be expressed as \ [2 \ times10 ^ 2 + 5 \ times10 ^ 1 + 4 \ times10 ^ 0 \]

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