They are all different. For example, 2, 67, 354, 1009. Let's look at these numbers in detail.
2 consists of one digit, so this number is called single digit. Another example of single-digit numbers: 3, 5, 8.
67 consists of two digits, so this number is called double digit number. Example of two-digit numbers: 12, 35, 99.
Three digit numbers consist of three numbers, for example: 354, 444, 780.
Four digit numbers consist of four digits, for example: 1009, 2600, 5732.

Two digits, three digits, four digits, five digits, six digits, etc. numbers are called multi-digit numbers.

Number digits.

Consider the number 134. Each digit of this number has its own place. Such places are called discharges.

The number 4 takes the place or place of ones. The number 4 can also be called a number first category.
The number 3 occupies the place or tens place. Or the number 3 can be called a number second class.
And the number 1 occupies the hundreds place. In another way, the number 1 can be called the number third category. The number 1 is the last digit of the glory of the number 134, so the number 1 can be called the highest digit. The highest digit is always greater than 0.

Every 10 units of any rank form a new unit of a higher rank. 10 units form one tens place, 10 tens form one hundreds place, ten hundreds form one thousand place, etc.
If there is no digit, then it will be replaced by 0.

For example: the number 208.
The number 8 is the first digit of units.
The number 0 is the second tens place. 0 means nothing in mathematics. From the record it follows that this number does not have tens.
The number 2 is the third hundreds place.

This parsing of a number is called digit composition of the number.

Classes.

Multi-digit numbers are divided into groups of three digits from right to left. Such groups of numbers are called classes. The first class on the right is called class of units, the second one is called class of thousands, third - million class, fourth - class of billions, fifth - trillion class, sixth – class quadrillion, seventh - class quintillions, eighth – class sextillion.

Unit class– the first class on the right from the end is three digits consisting of a units place, a tens place and a hundreds place.
Class of thousands– the second class consists of the category: units of thousands, tens of thousands and hundreds of thousands.
Million class– the third class consists of the category: units of millions, tens of millions and hundreds of millions.

Let's look at an example:
We have the number 13,562,006,891.
This number has 891 units in the units class, 6 units in the thousands class, 562 units in the millions class, and 13 units in the billions class.

13 billion 562 million 6 thousand 891.

Sum of bit terms.

Anything having different digits can be decomposed into sum of bit terms. Let's look at an example:
Let's write the number 4062 into digits.

4 thousand 0 hundreds 6 tens 2 units or in another way you can write

4062=4 ⋅1000+0 ⋅100+6 ⋅10+2

Next example:
26490=2 ⋅10000+6 ⋅1000+4 ⋅100+9 ⋅10+0

The digits in multi-digit numbers are divided from right to left into groups of three digits each. These groups are called classes. In each class, the numbers from right to left indicate the units, tens and hundreds of that class:

The first class on the right is called class of units, second - thousand, third - millions, fourth - billions, fifth - trillion, sixth - quadrillion, seventh - quintillions, eighth - sextillion.

To make it easier to read the notation of a multi-digit number, a small space is left between the classes. For example, to read the number 148951784296, we highlight the classes in it:

and read the number of units of each class from left to right:

148 billion 951 million 784 thousand 296.

When reading a class of units, the word units is usually not added at the end.

Each digit in the notation of a multi-digit number occupies a certain place - position. The place (position) in the notation of a number on which the digit stands is called discharge.

The counting of digits goes from right to left. That is, the first digit on the right in a number is called the first digit, the second digit on the right is the second digit, etc. For example, in the first class of the number 148,951,784,296, digit 6 is the first digit, 9 is the second digit, 2 - third digit:

Units, tens, hundreds, thousands, etc. are also called bit units:
units are called units of the 1st category (or simple units)
tens are called units of the 2nd digit
hundreds are called 3rd digit units, etc.

All units except simple units are called constituent units. So, ten, hundred, thousand, etc. are composite units. Every 10 units of any rank constitutes one unit of the next (higher) rank. For example, a hundred contains 10 tens, a ten contains 10 prime units.

Any compound unit compared to another unit smaller than it is called unit of the highest category, and in comparison with a unit greater than it is called unit of the lowest category. For example, a hundred is a higher-order unit relative to ten and a lower-order unit relative to a thousand.

To find out how many units of any digit are in a number, you need to discard all the digits representing the units of lower digits and read the number expressed by the remaining digits.

For example, you need to find out how many hundreds there are in the number 6284, i.e. how many hundreds are in the thousands and hundreds of a given number together.

In the number 6284, the number 2 is in third place in the units class, which means there are two prime hundreds in the number. The next number to the left is 6, meaning thousands. Since every thousand contains 10 hundreds, 6 thousand contain 60 of them. In total, therefore, this number contains 62 hundreds.

The number 0 in any digit means the absence of units in this digit. For example, the number 0 in the tens place means the absence of tens, in the hundreds place - the absence of hundreds, etc. In the place where there is a 0, nothing is said when reading the number:

172 526 - one hundred seventy two thousand five hundred twenty six.
102 026 - one hundred two thousand twenty six.

Target: developing students' ability to read and write multi-digit numbers.

Tasks for the teacher:

• create conditions for students to develop practical skills in determining the ranks and classes of multi-digit numbers;
• organize learning activities in the classroom through collaboration with students;
• continue to develop the skills to think logically and express their thoughts, develop the cognitive interest of students by creating emotional situations in the lesson, situations of joy, entertainment;
• During the lesson, promote the development of such human qualities as kindness, responsiveness, and the desire to help.

Lesson type: a lesson in “discovering” new knowledge.

Methods and teaching technologies used: activity method technology, ICT.

Used forms of organizing students' cognitive activity: frontal, group, individual.

Equipment and main sources of information: PC, projector, lesson presentation, handouts. Textbook: G.V. Dorofeev, T.N. Mirakova, T.B. Buka “Mathematics” 4th grade.

Predicted results:

Subject:

• know the ranks and classes of multi-digit numbers;
• can read and write multi-digit numbers.

Metasubject:

• are able to set educational tasks and formulate conclusions.
• They know how to listen to their interlocutor and express their opinion.

Personal:

• are able to cooperate with the teacher and peers

During the classes

I. Psychological attitude towards activity.

Loud school bell
He called me back to class.
Be attentive and also diligent.

The children sat down at their desks. Look at each other, smile and wish each other good work.

The motto of our lesson: “ Don’t be hasty, but be patient.”

Today in the lesson we will go into the wonderful world of numbers. ( Slide 1)

II.Updating knowledge about the bit composition of three-digit numbers.

You already know a lot about numbers.

What signs are used to write numbers? (Numbers)

What numbers do you know? (Single-digit, two-digit, three-digit)

Why do they have such names? (1, 2 or 3 digits are used to write them)

What can you say about the number 1000? (It is four-digit, round)

Read the numbers and name the digit terms in them: 345, 67, 129, 921, 840. (Slide 2).

Look at the numbers and name the extra number: 145, 51, 512, 152, 521, 251, 5127. (Slide 3). Prove it.

Write these numbers in ascending order: (Slide 3)

What did you notice when looking at the rest of the numbers? (To write them, three numbers were used: 1, 2, 5);

What does the number 5 mean in each number?;

Draw a conclusion about the meaning of the digits in a number depending on the place it occupies.

III. Formulation of the problem. Setting goals and objectives for the lesson.

How many characters were used to write this number?

What needs to be done to make the number easy to read?

What do you think we will learn? (Read and write multi-digit numbers).

So, the topic of our lesson is “Digits and classes of numbers” (Slide 5)

IV. Work on the topic of the lesson.

1. Consider the table of ranks and classes. (Slide 6)

2. It should be viewed from right to left. First look at just the first column, first row.

What do you notice? (Here are three-digit numbers known to us)

Name the categories of class I:

1st category – units,

2nd category – tens,

3rd category – hundreds.

3. Read what the second grade of mathematicians was called? (Class of thousands), and III class?

(Million class).

Notice the names of the ranks of these classes? (Their names are the same as in 1st grade).

Yes, but when reading numbers you must say the name of the class.

Read the numbers written in the table.

V. Primary consolidation

1. Multimedia disc on the topic of the lesson. (Listen)

3. Tasks to be assigned to a multimedia disc.

4. Task No. 6 of the textbook p. 107 – commenting

5. Largest four-digit number? (9.999) How to write it down?

6. Smallest five-digit number? (10.000)

7. Biggest five-digit number? (99.999)

8. Biggest six-digit number? (1,000,000). Do you know why million is the word “giant”? Just imagine that if each sheet is read in 6 minutes and if you read for 8 hours continuously every day, except Sundays, then a million sheets can be read in only 40 years! That's what a million is! That's why they call him a giant!

9. Oral work based on presentation slides (Slides 7-11).

10. Primary consolidation of the ability to write numbers, followed by testing.

Write down the numbers: 6 thousand, 140 thousand, 5 million. (Check on slide 12)

Write in numbers: one hundred sixty-two thousand nine hundred thirty-five, one million three hundred eighty thousand three hundred one. (Check on slide 13)

VI. Physical education minute. (Slide 14)

VII. Consolidation.

Game 1 “Live numbering”

Three students go to the board, each receives a set of numbers.

The first shows the number of class III units,

the second is the number of units of class II tens,

the third is the number of class I units.

Students correctly name a multi-digit number.

Game 2 “Read the number”

Now everyone will think of a number (0-9) and 3 people from each row. They will come out and write it on the board and we will get a multi-digit number.

Read the number.

How many units of each class are there in this number?

How many units of each digit are there in this number?

Group work

Before you start working in a group, assign roles to each other. The group works under the motto: “You are responsible for what your group does.”

(Each group is given sets of numbers from which the largest and smallest numbers are made)

VIII. Repetition of what has been learned.

1. Problem No. 10 p. 108.

Checking the solution:

1) 100,000: 50 = 2000 (bags) - only on 2 machines.

2) 2000: 2 = 1000 (bags) - on each machine.

What class of numbers are used in the problem?

2. Test. (Slide 15)

Circle the number of the correct answer:

1. Thirteen thousand fifty six is

2. The number 32,028 is read:

1) three thousand two hundred twenty eight;

2) three hundred twenty thousand twenty eight;

3) thirty two thousand twenty eight.

3. The number 9,860 consists of the sum of its digit terms

2) 9000 + 800 + 60

4. A number consisting of 10 thousand, 8 hundreds and 3 units is written:

5. A number in which 7 units of the first class and 3 units of the second class is written:

6. The number to which you need to add 1 to get 100,000:

Check in pairs, evaluate work according to criteria and evaluate yourself.

IX. Reflection

Remember everything we talked about in class and answer the questions:

What was the topic of the lesson?

What was I supposed to learn in the lesson? (target)

What happened?

What didn't work and why?

X. Homework(multi-level)

Homework for “5”. (cards)

1. Write three different six-digit numbers using only the numbers 5, 0.7. Underline the largest of the numbers written down. Write it down as a sum of bit terms.

2. Write it down three-digit number. Change the numbers of units and hundreds in it. Write down the resulting number.

Homework for “4”. (cards)

1. Write down the number that contains:

a) 500 units. 3 classes, 50 units. 2 classes and 5 units. 1st class;

b) 6 units. 2 classes and 172 units. 1st class.

2. Continue the series of numbers. Add 5 more numbers: 72100, 73200, 74300, ...

In the names of Arabic numbers, each digit belongs to its own category, and every three digits form a class. Thus, the last digit in a number indicates the number of units in it and is called, accordingly, the ones place. The next, second from the end, digit indicates the tens (tens place), and the third from the end digit indicates the number of hundreds in the number - the hundreds place. Further, the digits are repeated in the same way in turn in each class, already denoting units, tens and hundreds in the classes of thousands, millions, and so on. If the number is small and does not have a tens or hundreds digit, it is customary to take them as zero. Classes group digits in numbers of three, often placing a period or space between classes in computing devices or records to visually separate them. This is done to make it easier to read. large numbers. Each class has its own name: the first three digits are the class of units, followed by the class of thousands, then millions, billions (or billions), and so on.

Since we use the decimal system, the basic unit of quantity is ten, or 10 1. Accordingly, as the number of digits in a number increases, the number of tens also increases: 10 2, 10 3, 10 4, etc. Knowing the number of tens, you can easily determine the class and rank of the number, for example, 10 16 is tens of quadrillions, and 3 × 10 16 is three tens of quadrillions. The decomposition of numbers into decimal components occurs in the following way - each digit is displayed in a separate term, multiplied by the required coefficient 10 n, where n is the position of the digit from left to right.
For example: 253 981=2×10 6 +5×10 5 +3×10 4 +9×10 3 +8×10 2 +1×10 1

The power of 10 is also used in writing decimal fractions: 10 (-1) is 0.1 or one tenth. In a similar way to the previous paragraph, you can also expand a decimal number, n in this case will indicate the position of the digit from the decimal point from right to left, for example: 0.347629= 3×10 (-1) +4×10 (-2) +7×10 (-3) +6×10 (-4) +2×10 (-5) +9×10 (-6 )

Names of decimal numbers. Decimal numbers are read according to the last digit after the decimal point, for example 0.325 - three hundred twenty-five thousandths, where the thousandths is the digit of the last digit 5.

Table of names of large numbers, digits and classes

To remember how much harvest they harvested or how many stars there were in the sky, people came up with symbols. These symbols were different in different areas.

But with the development of trade, in order to understand the designations of another people, people began to use the most convenient symbols. For example, we use Arabic symbols. And they are called Arab because Europeans learned them from the Arabs. But the Arabs learned these symbols from the Indians.

The symbols that are used to write numbers are called in numbers .

The word number comes from the Arabic name for the number 0 (sifr). This is a very interesting figure. It is called insignificant and denotes the absence of something.

In the picture we see a plate with 3 apples on it and an empty plate with no apples on it. In the case of an empty plate, we can say that there are 0 apples on it.

The remaining numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 are called meaningful .

Bit units

Notation the one we use is called decimal. Because it is precisely ten units of one category that constitute one unit of the next category.

We count in units, tens, hundreds, thousands, and so on. These are the digit units of our number system.

10 ones – 1 ten (10)

10 tens – 1 hundred (100)

10 hundreds – 1 thousand (1000)

10 times 1 thousand – 1 ten thousand (10,000)

10 tens of thousands – 100 thousand (100,000) and so on...

Place is the place of a digit in a number notation.

For example, among 12 two digits: the ones digit consists of 2 units, the tens place consists of one dozen.

We talked about how 0 is an insignificant number that means the absence of something. In numbers, the number 0 indicates the absence of ones in the digit.

In the number 190, the digit 0 indicates the absence of a ones place. In the number 208, the digit 0 indicates the absence of a tens place. Such numbers are called incomplete .

And numbers whose digits do not have zeros are called full .

The digits are counted from right to left:

It will be clearer if you depict the bit grid as follows:

1. Among 2375 :

5 units of the first category, or 5 units

7 units of the second digit, or 7 tens

3 units of the third category, or 3 hundreds

2 units of the fourth category, or 2 thousand

This number is pronounced like this: two thousand three hundred seventy five

1. Among 1000462086432

2 pieces

3 tens

8 tens of thousands

0 hundred thousand

2 units million

6 tens of millions

4 hundred million

0 units billion

0 tens of billions

0 hundred billion

1 unit trillion

This number is pronounced like this: one trillion four hundred sixty two million eighty six thousand four hundred thirty two .

1. Among 83 :

3 units

8 tens

Pronounced like this: eighty three .

bit, call numbers consisting of units of only one digit:

For example, numbers 1, 3, 40, 600, 8000 - bit numbers, in such numbers there can be as many zeros (insignificant digits) as desired or not at all, but there is only one significant digit.

Other numbers, for example: 34, 108, 756 and so on, unbited , they are called algorithmic.

Non-digit numbers can be represented as a sum of digit terms.

For example, number 6734 can be represented like this:

6000 + 700 + 30 + 4 = 6734