Decimal and place value systems, what is decimal

An important goal of the fourth-grade "Multi-Digit Cognition" is to enable students to further understand the place-value system and the decimal system, and the idea of place-value system and decimal system is very important in the learning of numbers. The study of place-value and decimal systems should not stop at memorizing the names of digits and being able to read and write numbers, but should develop students' true understanding of them in a variety of ways. To this end, efforts have been made in the following areas:

On the basis of the introduction of the intuitive model of "individual", "ten", "hundred" and "thousand" counting units in the first section, the textbook gives the model of "ten thousand", and uses the "intuitive model of counting units" to represent the relationship between counting units. At the same time, the textbook corresponds to the intuitive model of counting units, counters and abstract symbols, which not only realizes gradual abstraction, but also helps students to experience the meaning of numbers from different perspectives, helps students master a variety of tools to explore and solve problems, and helps students experience the connection between numbers and shapes. The textbook is designed with the content of "Do you know how big 100,000 is 100,000", which can develop students' feelings about large numbers, with the help of 2,000 classes that are relatively easy to feel, so that students can experience the number of 100,000 students, and through the height of a three-story building that can be observed, students can experience the thickness of 100,000 sheets of paper, so that abstract large numbers can be understood by students through imagination and reasoning.

At the same time, when students feel "100,000", they can use their familiar objects to constantly compare them, such as how many people are 100 people to know how many people are 1,000 people, how many people are to deduce 10,000 people from 1,000 people, and then feel how many people are 100,000 people. With the help of layer-by-layer comparisons in the process of practical problems, students will once again feel the relationship between hundreds, thousands, thousands, and hundreds of thousands, and further understand the place-value system and the decimal system. At the same time, the textbook also arranges math reading:

Starting from the knotted rope counting, combined with ** and words to introduce the development process of human representations, not only enables students to understand the role of social development in promoting the development of mathematics, as well as the role of mathematics in the progress of human society and the development of human civilization, but also in the comparison of different counting symbols, students will further appreciate the characteristics and advantages of the place value system and the decimal system. In short, it is a striking feature of the textbooks in the new century that they should use a variety of angles and methods to design a variety of activities and portray important concepts and ideas so that students can gain a better understanding.

The place-value system is the value represented by each number, which depends not only on the number itself, but also on its position in the counting1For example, in the decimal value system, it is also a number"2", put it in the single place to mean 2, put it in the ten place to mean 20 (2 10), put it in the hundred place to mean 200 (2 10 2), put it in the thousand place to mean 2000 (2 10 3).

2.For example, in the binary value system, 1 in the single place means 1, placed in the 10 place means 2 (1*2), and placed in the hundred place means 4 (1*2 2). Because there is not only base 10, but also base 2, base 8, base hexadecimal, etc., so the two are different

Decimal numbers are marked with .9 , these ten numbers are indicated. The decimal system (notation) is a number system based on 10 and is the most widely used carry system in the world.

That is, full of ten into one, full of twenty into two, and so on; According to the right, the first right is 10 0, and the second right is 10 1??And so on, the nth digit 10 (n-1), the value of this number is equal to the sum of the value of each bit * the corresponding weight of that bit.

The vast majority of ancient civilizations in the world used the decimal system, ancient China, ancient India, ancient Greece, etc. There are, of course, exceptions, such as the Sumerians using the decimal system, the Mayans using the decimal system, and the ancient Babylonians using the decimal system.

Two-decimal system.

Binary-coded-decimal is also known as binary-decimal (BCD>One of the counting methods of computers is binary-encoded decimal. The encoding of a decimal data bit is directly represented by the numeric value of four binary bits, called a BCD code.

The BCD code is divided into 8421 yards, 2421 yards and 3 yards, and Gray yards.

etc., but the most commonly used is 8421 code, 8, 4, 2, 1 respectively represent four-digit binary numbers.

The weight of each of you from high to low. This symbology from. The notation to 9 is shown in the table.

Numbers have different decimal systems for different industry uses, and the numbers used on a daily basis are all in decimal and are composed of 0-9.

Computers use binary because they can only use two states, which consists of 0,1.

In addition, there are occimal and hexadecimal, all of which are related to computers.

Bits are simple. The daily ten hundred thousand refer to the bit. 2-digit decimal number. It's a decimal number between 10-99.

Decimal numbers are a system of numbers based on 10, consisting of ten basic numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal system, the English name is decimal system, ** in the Greek decem, meaning ten.

The decimal place-value notation includes two principles: the decimal place value system and the place-value system"Decimal"That is, full of ten into one; "Place value"It means that the same number represents different values in different positions, such as three digits"111", on the right"1"In the single digit it represents 1 one, in the middle"1"In the ten place, it means 1 ten, on the left"1"In the hundreds, it means 1 hundred. In this way, the extremely difficult representation and calculus of integers are so easy and easy that the crucial role it plays in the development of mathematics is often overlooked.

Principle of use: The decimal system is based on the two principles of decimal and decimal places, that is, all numbers are represented by 10 basic symbols, full decimal one, and the same symbol represents different values in different positions, and the position of the symbol is very important. The basic symbols are ten numbers from 0 to 9.

To represent 10 times these ten numbers, move the numbers one place to the right and fill in the empty spaces with 0, i.e. 10, 20, 30 ,..90；To represent 10 times these ten numbers, continue to move the numbers to the left, i.e., 100, 200, 300 ,..To represent the 1 10 of a number, move the number to the right, and fill in the empty space with 0 if needed

1 10 bits, 1 100 for 1 1000 bits.

Hello, glad for your question. First of all, let's take the decimal system that we are more familiar with as an example. Why does the decimal 123 read one hundred and twenty-three?

Because 1 is in the hundred, 2 in the ten, and 3 in the single place. That is, 123 = 1 * 100 + 2 * 10 + 3 * 1, where the sum of 1 is the bit weight of the hundred, ten and single digits respectively. It can be seen that the weight of the nth bit of the integer part is the n-1 power of 10, and so on, the weight of the mth bit of the decimal part is the -m power of 10.

Then for binary, the bit weight of the nth bit of the integer part is the n-1 power of 2, and the bit weight of the mth bit of the decimal part is the -m power of 2.

Hello, glad for your question.

Decimal. Convert to hexadecimal.

The rule of division of the integer part by 16 is the remainder, take out the remainder of each time, until the quotient is 0, and the final remainder is the high position.

So 29 divided by 16, the quotient is 1, and the remainder is 13; 1 divided by 16, the quotient is 0, and the remainder is 1. So the result is 1 13, and in hexadecimal 13 is represented by d, so the final result is 1d.

The rate of advance between each of the two adjacent counting units is ten. That is, decimal.

The units of counting of integers are described in the question.

In addition, in addition to decimal (i.e., every decimal one), there are binary, octal, hexadecimal, and so on. Numbers between different decimal systems can be converted to each other by formulas. Generally, decimal conversion is used for information processing and other work, such as the computer converts the decimal used by humans into the binary used by the computer itself, and then converts the result into decimal to present the result.