Each rank. Decimal number system, classes and ranks of natural numbers

A pronoun is a special class of significant words that indicate an object without naming it. To avoid tautology in speech, the speaker can use a pronoun. Examples: I, yours, who, this, everyone, most, all, myself, mine, other, another, that, somehow, someone, something, etc.

As can be seen from the examples, pronouns are most often used instead of a noun, as well as instead of an adjective, numeral or adverb.

Pronouns are typically divided into categories according to meaning. This part of speech is focused on names. In other words, pronouns replace nouns, adjectives, and numerals. However, the peculiarity of pronouns is that, replacing names, they do not acquire their meaning. According to established tradition, only modifiable words are considered pronouns. All unchangeable words are treated as pronominal adverbs.

This article will present the meaning and grammatical features, as well as examples of sentences in which certain pronouns are used.

Table of pronouns by category

Personal pronouns	I, you, we, you, he, she, it, they
Reflexive pronoun
Possessive pronouns	my, yours, ours, yours, yours
Demonstrative pronouns	this, that, such, so much
Determinative pronouns	himself, most, all, every, each, any, other, other
Interrogative pronouns	who, what, which, which, whose, how many, which
Relative pronouns	who, what, how, which, which, whose, how many, which
Negative pronouns	no one, nothing, none, nobody, no one, nothing
Indefinite pronouns	someone, something, some, some, several, some, anyone, anyone, anything, some, some

Pronouns are divided into three categories:

Pronominal nouns.
Pronominal adjectives.
Pronominal numerals.

Personal pronouns

Words indicating persons and objects that are participants in a speech act are called “personal pronouns.” Examples: I, you, we, you, he, she, it, they. I, you, we, you denote participants in verbal communication. The pronouns he, she, they do not participate in the speech act; they are reported to the speaker as non-participants in the speech act.

I know what you want to tell me. (Participant in a speech act, object.)
You should read the whole thing fiction from the list. (The subject to whom the action is directed.)
We had a wonderful holiday this year! (Participants in a speech act, subjects.)
You played your role perfectly! (Addressee, object to which the address is directed in a speech act.)
He prefers a quiet pastime. (Non-participant in the speech act.)
Will she definitely go to America this summer? (Non-participant in the speech act.)
They jumped with a parachute for the first time in their lives and were very pleased. (Non-participant in the speech act.)

Attention! The pronouns his, her, their, depending on the context, can be used both as possessive and personal pronouns.

Compare:

He was not at school today, neither for the first nor for the last lesson. - His performance at school depends on how often he attends classes. (In the first sentence it is a personal pronoun in genitive case, in his second sentence - possessive pronoun.)
I asked her to keep this conversation between us. “She ran, her hair fluttered in the wind, and her silhouette was getting lost and lost with every second, moving away and dissolving in the light of day.
You should always ask them to turn the music down. “Their dog very often howls at night, as if grieving for some unbearable grief of his.

Reflexive pronoun

The pronoun oneself belongs to this category - it indicates the person of the object or addressee who is identified with actor. This function is performed by reflexive pronouns. Example sentences:

I have always considered myself the happiest in the whole wide world.
She constantly admires herself.
He doesn't like to make mistakes and trusts only himself.

Can I keep this kitten with me?

Possessive pronouns

A word indicating that a person or thing belongs to another person or thing is called a “possessive pronoun.” Example: mine, yours, ours, yours, yours. Possessive pronouns indicate belonging to the speaker, interlocutor or non-participant in the act of speech.

My the decision always turns out to be the most correct.
Yours wishes will definitely be fulfilled.
Our The dog behaves very aggressively towards passers-by.
Is yours the choice will be yours.
Finally I got mine present!
Their keep your thoughts to yourself.
My the city misses me and I feel how much I miss it.

Words like her, him, them can act as a personal pronoun in or as possessive pronoun. Example sentences:

Their the car is parked at the entrance. - They were not in the city for 20 years.
His the bag is lying on the chair. - He was asked to bring tea.
Her the house is located in the city center. - She was made the queen of the evening.

The possessive pronoun also indicates that a person (object) belongs to a group of objects. Example:

Our I will remember our joint trips for a long time!

Demonstrative pronouns

The demonstrative is the second name that bears the demonstrative pronoun. Examples: this, that, such, so much. These words distinguish this or that object (person) from a number of other similar objects, persons or signs. This function is performed by the demonstrative pronoun. Examples:

This The novel is much more interesting and informative than all those I have read before. (Pronoun this distinguishes one object from a number of similar ones, indicates the peculiarity of this object.)

Pronoun This also performs this function.

This sea, these mountains, This the sun will forever remain in my memory as the brightest memory.

However, you should be careful when determining the part of speech and not confuse the demonstrative pronoun with a particle!

Compare examples of demonstrative pronouns:

This it was excellent! - Did you play the role of a fox in a school play? (In the first case, This is a pronoun and fulfills the predicate. In the second case This- particle and syntactic role is not in the sentence.)
That the house is much older and more beautiful than this one. (Pronoun That highlights an object, points to it.)
Neither such, no other option suited him. (Pronoun such helps to concentrate attention on one of many subjects.)
So many once he stepped on the same rake, and again repeats everything all over again. (Pronoun so many emphasizes the repetition of the action.)

Determinative pronouns

Examples of pronouns: himself, most, all, every, each, any, other, other. This category is divided into subcategories, each of which includes the following pronouns:

1.Himself, the most- pronouns that have an excretory function. They elevate the object in question and individualize it.

Myself the director, Alexander Yaroslavovich, was present at the party.
He was offered the most a highly paid and prestigious job in our city.
The most The greatest happiness in life is to love and be loved.
Self Her Majesty condescended to praise me.

2.All- a pronoun that has the meaning of breadth of coverage of the characteristics of a person, object or characteristic.

All the city came to see him perform.
All The road passed in remorse and the desire to return home.
All the sky was covered with clouds, and not a single clearing was visible.

3. Anyone, everyone, anyone- pronouns denoting freedom of choice from several objects, persons or characteristics (if they exist at all).

Semyon Semenovich Laptev is a master of his craft - this is for you any will say.
Any a person is capable of achieving what he wants, the main thing is to make an effort and not be lazy.
Each blade of grass every the petal breathed life, and this desire for happiness was transmitted to me more and more.
All sorts of things the word he said turned against him, but he did not seek to correct it.

4.Different, different- pronouns that have meanings that are not identical to what was said earlier.

I chose other a path that was more accessible to me.
Imagine another If you were me, would you do the same?
IN other Once he comes home, silently, eats and goes to bed, today everything was different...
The medal has two sides - another I did not notice.

Interrogative pronouns

Examples of pronouns: who, what, which, which, whose, how many, which.

Interrogative pronouns contain questions about persons, objects or phenomena, quantities. A question mark is usually placed at the end of a sentence that contains an interrogative pronoun.

Who was that man who came to see us this morning?
What what will you do when the summer exams are over?
What there should be a portrait of an ideal person, and how do you imagine him?
Which out of these three people could know what really happened?
Whose is this a briefcase?
How much does a red dress cost? which did you come to school yesterday?
Which your favorite time of year?
Whose I saw a child in the yard yesterday?
How Do you think I should enroll in the Faculty of International Relations?

Relative pronouns

Examples of pronouns: who, what, how, which, which, whose, how many, which.

Attention! These pronouns can act as both relative and interrogative pronouns, depending on whether they are used in a particular context. In a complex sentence (CSS), only the relative pronoun is used. Examples:

How are you making sponge cake with cherry filling? - She told how she prepares a pie with cherry filling.

In the first case How - the pronoun has an interrogative function, i.e. the subject concludes a question about a certain object and the method of obtaining it. In the second case, the pronoun How is used as a relative pronoun and acts as a connecting word between the first and second simple sentences.

Who knows in which does the sea flow into the Volga River? “He didn’t know who this man was and what could be expected from him.
What do you need to do in order to get a job? Good work? - He knew what to do in order to get a well-paid job.

What- pronoun - used both as a relative and as an interrogative pronoun, depending on the context.

What what are we going to do tonight? - You said that today we should visit our grandmother.

To accurately determine the category of pronouns when choosing between relative and interrogative, you need to remember that the interrogative pronoun in a sentence can be replaced by a verb, a noun, or a numeral, depending on the context. The relative pronoun cannot be replaced.

What do you want for dinner today? - I would like vermicelli for dinner.
Which do you like the color? - Purple do you like it?
Whose is this a house? - Is this mom's house?
Which are you in line? -Are you eleventh in line?
How many do you have any candy? - Do you have six sweets?

The situation is similar with the pronoun than. Compare examples of relative pronouns:

What to do on the weekend? - He completely forgot what I wanted to do this for the weekend. (As we see, in the second version the pronoun how is included in the category of relative and performs a connecting function between two parts of a complex sentence.)
How did you get into my house yesterday? - Anna Sergeevna looked questioningly at the boy and did not understand how he got into her house.
How does it feel to realize that you are in trouble? - I know from myself what it’s like to realize that your plans are collapsing quickly and irrevocably.
How many times do I ask you not to do this again? “She has already lost count of the number of times her son brought his class teacher to tears.
Whose car is parked at the gate of my house? “He was at a loss, so he couldn’t figure out whose idea it was to provoke a fight.
How much is this Persian kitten worth? - He was told how much a red Persian kitten costs.
Who knows what year the Battle of Borodino took place? - Three students raised their hands: they knew in what year the Battle of Borodino took place.

Some scholars propose to combine relative and interrogative pronouns into one category and call them “interrogative-relative pronouns.” Examples:

Who is there? - He didn't see who was here.

However, at present it has not yet been possible to reach a general agreement, and the categories of interrogative and relative pronouns continue to exist separately from each other.

Negative pronouns

Examples of pronouns: no one, nothing, none, nobody, no one, nothing. Negative pronouns mean the absence of persons, objects, and also to indicate their negative characteristics.

Nobody didn't know what to expect from him.
Nothing he was not interested enough to devote his whole life to this matter.
No debt and none money couldn't keep him from running away.
A lonely dog ran along the road, and it seemed that it never had an owner, a home or tasty food in the morning; She was draw.
He tried to find excuses for himself, but it turned out that everything happened precisely on his initiative, and no one was to blame for this.
He was completely nothing to do, so he walked slowly in the rain past the glowing shop windows and watched the oncoming cars passing by.

Indefinite pronouns

An indefinite pronoun is formed from interrogative or relative pronouns. Examples: someone, something, some, some, several, some, anyone, anyone, anything, some, some. Indefinite pronouns contain the meaning of an unknown, undefined person or thing. Also, indefinite pronouns have the meaning of deliberately hidden information that the speaker specifically does not want to communicate.

Examples for comparison:

Someone's a voice rang out in the darkness, and I didn’t quite understand who it belonged to: a man or an animal. (Lack of information from the speaker.) - This letter was from my no one friend who for a long time was absent from our city and was now planning to come. (Information deliberately hidden from listeners.)
Something the incredible happened that night: the wind tore and tossed leaves from the trees, lightning flashed and pierced the sky. (Instead of something You can substitute indefinite pronouns with similar meaning: something, something.)
Some of my friends consider me a strange and wonderful person: I don’t strive to earn a lot of money and live in a small old house on the edge of the village . (Pronoun some can be replaced by the following pronouns: some, several.)
Some a pair of shoes, a backpack and a tent were already packed and were waiting for us to pack up and leave far, far from the city. (The subject does not specify the number of objects, but generalizes their number.)
Some people informed me that you received the letter, but do not want to acknowledge it volume.(The speaker deliberately hides all information about the face.)
If anyone I saw this man, please report this to the police!
Anyone knows what Natasha Rostova and Andrei Bolkonsky talked about at the ball?
When will you see anything interesting, don’t forget to write down your observations in a notebook.
Some points in studying in English remained incomprehensible to me, then I returned to the previous lesson and tried to go through it again. (Intentional concealment of information by the speaker.)
How long I still had some money in my wallet, but I didn’t remember how much. (Lack of information about the subject from the speaker.)

Grammatical grades of pronouns

Grammatically, pronouns are divided into three categories:

Pronominal noun.
Pronominal adjective.
Pronominal numeral.

TO pronominal noun These categories of pronouns include: personal, reflexive, interrogative, negative, indefinite. All these categories are similar in their grammatical properties to nouns. However, pronominal nouns have certain features that a pronoun does not have. Examples:

I came to you . (In this case, this is the masculine gender, which we determined by the past tense verb with a zero ending). - You came to me. (Gender is determined by the ending of the verb “came” - feminine,

As you can see from the example, some pronouns do not have a gender category. In this case, the genus can be restored logically, based on the situation.

Other pronouns of the listed categories have a gender category, but it does not reflect the real relationships of persons and objects. For example, the pronoun Who always combined with a verb in the masculine past tense.

Who was the first woman to travel into space?
Ready or not, here I come.
She knew who would be the next contender for her hand and heart.

The pronoun that is used with neuter nouns of the past tense.

What allowed you to do this act?
He had no idea that something similar to his story could be happening somewhere.

Pronoun He has generic forms, but gender here acts as a classification form, and not as a nominative form.

TO pronominal adjective These include demonstrative, attributive, interrogative, relative, negative, and indefinite pronouns. They all answer the question Which? and are likened to adjectives in their properties. They have dependent forms of number and case.

This tiger cub is the fastest in the zoo.

Pronominal numerals include pronouns as much as, several. They are likened to numerals in their meaning when combined with nouns.

How many books have you read this summer?
I now had so many opportunities!
My grandmother left some hot pies for me.

Attention! However, in combination with verbs, pronouns how many, as many, several are used as adverbs.

How much is this orange blouse worth?
You can only spend that much on vacation.
I thought a little about how to live and what to do next.

The world of pronouns diverse and very wide. There is probably no language that does not have pronouns. We constantly use them in our speech, so after nouns and verbs pronouns rank 3rd in frequency of use. However, it should be borne in mind that, in comparison with verbs and nouns, of which there are thousands in the language, there are only a few dozen pronouns. Now imagine how often we use the same pronouns in our conversation or in written texts! The most frequent pronouns are: I, what, he, this, you, we, this, she, they, all, then, all, my, which.

Of course, the question may arise: “Why repeat pronouns so often? Can’t they be replaced with other parts of speech?” No, you cannot do without pronouns, and their frequent repetition is also inevitable, because the need constantly arises to point out events, objects, phenomena, quantities, qualities that have already been mentioned earlier. If there were no pronouns, we would be forced to repeat nouns, adjectives, numerals, verbs and even entire phrases, and this is too tedious and long. The language, like most people, is quite lazy, that's why pronouns are needed - to save space, time and space.

Pronouns- This words that do not name an object, attribute or quantity, but only indicate it. Pronouns, therefore, are not specific lexical meaning, A generalized. But in context, a pronoun can take on a specific meaning, which will change in a different context. For example, the pronoun He in sentences " The ball fell, it was light" And " The brick fell, it was heavy"will have different lexical meaning in accordance with what exactly replaces the pronoun he – noun ball or noun brick.

However, not all pronouns can be specified in a certain context. Some always retain their meaning only as a pointer to an object, attribute, quantity. This applies primarily to negative And indefinite pronouns. For example: Nobody he won’t be able to learn the rules for Varenka.

By value pronouns accepted divided into nine categories. Enough a large number of These categories cause certain difficulties when studying, but the main thing is to understand the principle of division and the meaning of pronouns, then it will be much easier to learn.

1. Personal pronouns. I - we, you - you, he, she, it - they.

Example: Veronica won't come. She studies Russian with a tutor.

2. Reflexive pronoun myself . It indicates the subject's attitude towards himself.

!!! This is a pronoun Not has nominative case forms, has no gender and number. Example: Everyone needs to look at least once myself from the outside.

3. Possessive pronouns.Mine, yours, ours, yours, yours.

These pronouns, like possessive adjectives, denote affiliation.

Example: Take it my Russian language textbook.

4. Demonstrative pronouns.That (that, that, those), such (such, such, such), this (this, this, these); such, such, such (such), such (such), this, that, so much.

All these pronouns except the pronoun so many , can have the category of gender, number and case. Pronoun so many Maybe only change according to cases.

Example: Be sure to learn these pronoun ranks!

5. Interrogative pronouns.Who, what, which, which, which, whose, how many, which.

These pronouns are used in interrogative sentences to formulate a question.

Example: Who Are you ready to study seriously and persistently?

6. Relative pronouns. Who, what, which, which, which, whose, how many, which, which.

These pronouns homonymous with interrogative, but it is not difficult to distinguish them: relative used in complex sentences as a means subordinating connection subordinate part of a sentence with the main one. Here they are usually called allied words.

Example: I know, Who ready to work seriously and persistently.

Sometimes relative and interrogative pronouns are combined into one category: interrogative-relative.

7. Determinative pronouns. All, every (every, everyone), himself, most, each, other, any, other.

Example: I myself I want to achieve everything.

8. Negative pronouns.Nobody, nothing, no one, nothing, none, no one.

The meaning of negative pronouns not revealed in context, which is their feature.

All negative pronouns are formed from interrogatives using prefixes neither- And Not- . Console Not- always percussive, and the prefix neither- always without accent.

Example: Once get sick, never do not be sick.

Remember! Pronouns no one And nothing do not have a nominative case form!

9. Indefinite pronouns.Somebody, somebody, somebody, somebody, somebody; something, something, something, anything, anything; some, which, which, some, some, some, any, any; someone's, someone's, anyone's; some.

General OS The peculiarity of indefinite pronouns, as well as negative ones, is that their meaning is not revealed in context.

Indefinite pronouns are formed from interrogatives using attachments something, Not- and postfixes -this, -either, -something.

Example: Anyone will help me solve this problem.

Remember! Pronoun someone used only in the nominative case, pronoun something – in the nominative and accusative cases. In fact, these pronouns do not change!

So, you have a difficult but doable task - to understand and learn the ranks of pronouns by meaning. If you can handle it, it will be much easier for you when studying complex sentences.

Good luck to you and a beautiful, competent Russian language!

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Our first lesson was called numbers. We have covered only a small part of this topic. In fact, the topic of numbers is quite extensive. It has a lot of subtleties and nuances, a lot of tricks and interesting features.

Today we will continue the topic of numbers, but again we will not consider it all, so as not to complicate learning with unnecessary information, which at first is not really needed. We'll talk about discharges.

Lesson content

What is a discharge?

If we talk in simple language, then the digit is the position of the digit in the number or the place where the digit is located. Let's take the number 635 as an example. This number consists of three digits: 6, 3 and 5.

The position where the number 5 is located is called units digit

The position where the number 3 is located is called tens place

The position where the number 6 is located is called hundreds place

Each of us has heard from school such things as “units”, “tens”, “hundreds”. The digits, in addition to playing the role of the position of the digit in the number, tell us some information about the number itself. In particular, the digits tell us the weight of the number. They tell you how many units, how many tens, and how many hundreds there are in a number.

Let's return to our number 635. In the ones place there is a five. What does this mean? And this means that the ones digit contains five ones. It looks like this:

In the tens place there is a three. This tells us that the tens place contains three tens. It looks like this:

There is a six in the hundreds place. This means that there are six hundreds in the hundreds place. It looks like this:

If we add up the number of resulting units, the number of tens and the number of hundreds, we get our original number 635

There are also higher digits such as the thousand digit, the tens of thousands digit, the hundreds of thousands digit, the millions digit and so on. We will rarely consider such large numbers, but nevertheless it is also desirable to know about them.

For example, in the number 1645832, the units digit contains 2 ones, the tens digit contains 3 tens, the hundreds digit contains 8 hundreds, the thousands digit contains 5 thousand, the tens of thousands digit contains 4 tens of thousands, the hundreds of thousands digit contains 6 hundred thousand, and the millions digit contains 1 million. .

At the first stages of studying digits, it is advisable to understand how many units, tens, hundreds a particular number contains. For example, the number 9 contains 9 ones. The number 12 contains two ones and one ten. The number 123 contains three ones, two tens and one hundred.

Grouping items

After counting certain items, ranks can be used to group these items. For example, if we count 35 bricks in the yard, then we can use discharges to group these bricks. In the case of grouping objects, the ranks can be read from left to right. Thus, the number 3 in the number 35 will indicate that the number 35 contains three tens. This means that 35 bricks can be grouped three times in ten pieces.

So, let’s group the bricks three times ten pieces each:

It turned out to be thirty bricks. But there are still five units of bricks left. We will call them as "five units"

The result was three dozen and five units of bricks.

And if we did not group the bricks into tens and ones, then we could say that the number 35 contains thirty-five units. This grouping would also be acceptable:

The same can be said about other numbers. For example, about the number 123. Earlier we said that this number contains three units, two tens and one hundred. But we can also say that this number contains 123 units. Moreover, you can group this number in another way, saying that it contains 12 tens and 3 ones.

Words units, tens, hundreds, replace the multiplicands 1, 10 and 100. For example, in the units place of the number 123 there is a digit 3. Using the multiplicand 1, we can write that this unit is contained in the ones place three times:

100 × 1 = 100

If we add up the results of 3, 20 and 100, we get the number 123

3 + 20 + 100 = 123

The same thing will happen if we say that the number 123 contains 12 tens and 3 ones. In other words, the tens will be grouped 12 times:

10 × 12 = 120

And units three times:

1 × 3 = 3

This can be understood from the following example. If there are 123 apples, then you can group the first 120 apples 12 times, 10 each:

It turned out to be one hundred and twenty apples. But there are still three apples left. We will call them as "three units"

If we add the results of 120 and 3, we again get the number 123

120 + 3 = 123

You can also group 123 apples into one hundred, two tens and three ones.

Let's group a hundred:

Let's group two dozen:

Let's group three units:

If we add up the results of 100, 20 and 3, we again get the number 123

100 + 20 + 3 = 123

And finally, let's consider the last possible grouping, where the apples will not be distributed into tens and hundreds, but will be collected together. In this case, the number 123 will be read as "one hundred twenty-three units" . This grouping would also be acceptable:

1 × 123 = 123

The number 523 can be read as 3 units, 2 tens and 5 hundreds:

1 × 3 = 3 (three units)

10 × 2 = 20 (two tens)

100 × 5 = 500 (five hundred)

3 + 20 + 500 = 523

Another number 523 can be read as 3 ones 52 tens:

1 × 3 = 3 (three units)

10 × 52 = 520 (fifty two tens)

3 + 520 = 523

You can also read it as 523 units:

1 × 523 = 523 (five hundred twenty-three units)

Where to apply the discharges?

Bits make some calculations much easier. Imagine that you are at the board and solving a problem. You are almost finished with the task, all that remains is to evaluate the last expression and get the answer. The expression to be calculated looks like this:

I don’t have a calculator at hand, but I want to quickly write down the answer and surprise everyone with the speed of my calculations. Everything is simple if you add up the units separately, the tens separately and the hundreds separately. You need to start with the ones digit. First of all, after the equal sign (=) you need to mentally put three dots. These points will be replaced by a new number (our answer):

Now let's start folding. The ones place of the number 632 contains the number 2, and the ones place of the number 264 contains the number 4. This means the ones place of the number 632 contains two ones, and the ones place of the number 264 contains four ones. Add 2 and 4 units and get 6 units. We write the number 6 in the units place of the new number (our answer):

Next we add up the tens. The tens place of 632 contains the number 3, and the tens place of 264 contains the number 6. This means that the tens place of 632 contains three tens, and the tens place of 264 contains six tens. Add 3 and 6 tens and get 9 tens. We write the number 9 in the tens place of the new number (our answer):

And finally, we add up the hundreds separately. The hundreds place of 632 contains the number 6, and the hundreds place of 264 contains the number 2. This means that the hundreds place of 632 contains six hundreds, and the hundreds place of 264 contains two hundred. Add 6 and 2 hundreds to get 8 hundreds. We write the number 8 in the hundreds place of the new number (our answer):

Thus, if you add 264 to the number 632, you get 896. Of course, you will calculate such an expression faster and those around you will begin to be surprised at your abilities. They will think that you are quickly calculating large numbers, but you were actually calculating small ones. Agree that small numbers are easier to calculate than large ones.

Bit overflow

The digit is characterized by one digit from 0 to 9. But sometimes when calculating numerical expression a bit overflow may occur in the middle of a solution.

For example, when adding the numbers 32 and 14, no overflow occurs. Adding the units of these numbers will give 6 units in the new number. And adding tens of these numbers will give 4 tens in the new numbers. The answer is 46, or six ones and four tens.

But when adding the numbers 29 and 13, an overflow will occur. Adding the ones of these numbers gives 12 ones, and adding the tens gives 3 tens. If you write the resulting 12 units in the units place in a new number, and the resulting 3 tens in the tens place, you will get an error:

The value of the expression 29+13 is 42, not 312. What should you do if there is an overflow? In our case, the overflow occurred in the units digit of the new number. When we add nine and three units, we get 12 units. And in the units digit you can only write numbers in the range from 0 to 9.

The fact is that 12 units is not easy "twelve units" . Otherwise, this number can be read as "two ones and one ten" . The units digit is for ones only. There is no place for dozens there. This is where our mistake lies. By adding 9 units and 3 units we get 12 units, which can be called in another way two ones and one ten. By writing two ones and one ten in one place, we made a mistake, which ultimately led to an incorrect answer.

To correct the situation, two units need to be written in the ones place of the new number, and the remaining ten must be transferred to the next tens place. After adding two tens and one ten, we add to the result the ten that remained when adding the ones.

So, out of 12 units, we write two ones in the ones place of the new number, and move one ten to the next place

As you can see in the figure, we represented 12 units as 1 ten and 2 ones. We wrote two ones in the ones place of the new number. And one ten was transferred to the tens ranks. We will add this ten to the result of adding the tens of the numbers 29 and 13. In order not to forget about it, we wrote it above the tens of the number 29.

So, let's add up the tens. Two tens plus one ten is three tens, plus one ten, which remains from the previous addition. As a result, in the tens place we get four tens:

Example 2. Add the numbers 862 and 372 by digits.

We start with the ones digit. In the ones place of the number 862 there is a digit 2, in the ones place of the number 372 there is also a digit 2. This means that the ones place of the number 862 contains two ones, and the ones place of the number 372 also contains two ones. Add 2 units plus 2 units - we get 4 units. We write the number 4 in the units place of the new number:

Next we add up the tens. The tens place of 862 contains the number 6, and the tens place of 372 contains the number 7. This means that the tens place of 862 contains six tens, and the tens place of 372 contains seven tens. Add 6 tens and 7 tens and get 13 tens. A discharge has overflowed. 13 tens is a ten repeated 13 times. And if you repeat the ten 13 times, you get the number 130

10 × 13 = 130

The number 130 is made up of three tens and one hundred. We will write three tens in the tens place of the new number, and send one hundred to the next place:

As you can see in the figure, we represented 13 tens (the number 130) as 1 hundred and 3 tens. We wrote three tens in the tens place of the new number. And one hundred was transferred to the ranks of hundreds. We will add this hundred to the result of adding the hundreds of numbers 862 and 372. In order not to forget about it, we inscribed it above the hundreds of the number 862.

So let's add up the hundreds. Eight hundred plus three hundred is eleven hundred plus one hundred, which remains from the previous addition. As a result, in the hundreds place we get twelve hundred:

There is also an overflow in the hundreds place here, but this does not result in an error since the solution is complete. If desired, with 12 hundreds you can carry out the same actions as we did with 13 tens.

12 hundred is a hundred repeated 12 times. And if you repeat a hundred 12 times, you get 1200

100 × 12 = 1200

Of the 1200 there are two hundred and one thousand. Two hundred are written into the hundreds place of the new number, and one thousand is moved to the thousand place.

Now let's look at examples of subtraction. First, let's remember what subtraction is. This is an operation that allows you to subtract another from one number. Subtraction consists of three parameters: minuend, subtrahend, and difference. You also need to subtract by digits.

Example 3. Subtract 12 from 65.

We start with the ones digit. The ones place of the number 65 contains the number 5, and the ones place of the number 12 contains the number 2. This means that the ones place of the number 65 contains five ones, and the ones place of the number 12 contains two ones. Subtract two units from five units and get three units. We write the number 3 in the units place of the new number:

Now let's subtract the tens. In the tens place of the number 65 there is a digit 6, in the tens place of the number 12 there is a digit 1. This means that the tens place of the number 65 contains six tens, and the tens place of the number 12 contains one ten. Subtract one ten from six tens, we get five tens. We write the number 5 in the tens place of the new number:

Example 4. Subtract 15 from 32

The ones digit of 32 contains two ones, and the ones digit of 15 contains five ones. You cannot subtract five units from two units, since two units are less than five units.

Let's group 32 apples so that the first group contains three dozen apples, and the second group contains the remaining two units of apples:

So, we need to subtract 15 apples from these 32 apples, that is, subtract five ones and one ten apples. And subtract by rank.

You cannot subtract five units of apples from two units of apples. To perform a subtraction, two units must take some apples from an adjacent group (the tens place). But you can’t take as much as you want, since the dozens are strictly ordered in sets of ten. The tens place can only give two ones a whole ten.

So, we take one ten from the tens place and give it to two ones:

The two units of apples are now joined by one dozen apples. Makes 12 apples. And from twelve you can subtract five, you get seven. We write the number 7 in the units place of the new number:

Now let's subtract the tens. Since the tens place gave one ten to the units, now it has not three, but two tens. Therefore, we subtract one ten from two tens. There will be only one dozen left. Write the number 1 in the tens place of the new number:

In order not to forget that in some category one ten (or a hundred or a thousand) was taken, it is customary to put a dot above this category.

Example 5. Subtract 286 from 653

The ones digit of 653 contains three ones, and the ones digit of 286 contains six ones. You cannot subtract six ones from three units, so we take one ten from the tens place. We put a dot over the tens place to remember that we took one ten from there:

One ten and three ones taken together make thirteen ones. From thirteen units you can subtract six units to get seven units. We write the number 7 in the units place of the new number:

Now let's subtract the tens. Previously, the tens place of 653 contained five tens, but we took one ten from it, and now the tens place contains four tens. You cannot subtract eight tens from four tens, so we take one hundred from the hundreds place. We put a dot over the hundreds place to remember that we took one hundred from there:

One hundred and four tens taken together make fourteen tens. You can subtract eight tens from fourteen tens to get 6 tens. We write the number 6 in the tens place of the new number:

Now let's subtract hundreds. Previously, the hundreds place of 653 contained six hundreds, but we took one hundred from it, and now the hundreds place contains five hundred. From five hundred you can subtract two hundred to get three hundred. Write the number 3 in the hundreds place of the new number:

It is much more difficult to subtract from numbers like 100, 200, 300, 1000, 10000. That is, numbers with zeros at the end. To perform a subtraction, each digit has to borrow tens/hundreds/thousands from the next digit. Let's see how this happens.

Example 6

The ones digit of 200 contains zero ones, and the ones digit of 84 contains four ones. You cannot subtract four ones from zero, so we take one ten from the tens place. We put a dot over the tens place to remember that we took one ten from there:

But in the tens place there are no tens that we could take, since there is also a zero there. In order for the tens place to give us one ten, we must take one hundred from the hundreds place for it. We put a dot over the hundreds place to remember that we took one hundred from there for the tens place:

One hundred taken is ten tens. From these ten tens we take one ten and give it to the ones. This one ten taken and the previous zero ones together form ten ones. From ten units you can subtract four units to get six units. We write the number 6 in the units place of the new number:

Now let's subtract the tens. To subtract units, we turned to the tens place after one ten, but at that moment this place was empty. So that the tens place can give us one ten, we take one hundred from the hundreds place. We called this one hundred "ten tens" . We gave one ten to a few. So on this moment The tens place contains not ten, but nine tens. From nine tens you can subtract eight tens to get one ten. Write the number 1 in the tens place of the new number:

Now let's subtract hundreds. For the tens place, we took one hundred from the hundreds place. This means that now the hundreds category contains not two hundred, but one. Since there is no hundreds place in the subtrahend, we move this one hundred to the hundreds place of the new number:

Naturally, perform subtraction like this traditional method quite difficult, especially at first. Having understood the principle of subtraction itself, you can use non-standard methods.

The first way is to reduce a number that has zeroes at the end by one. Next, subtract the subtrahend from the result obtained and add the unit that was originally subtracted from the minuend to the resulting difference. Let's solve the previous example this way:

The number being reduced here is 200. Let's reduce this number by one. If you subtract 1 from 200, you get 199. Now in the example 200 − 84, instead of the number 200, we write the number 199 and solve the example 199 − 84. And solving this example is not particularly difficult. Let's subtract units from units, tens from tens, and simply transfer a hundred to a new number, since there are no hundreds in the number 84

We received the answer 115. Now to this answer we add one, which we initially subtracted from the number 200

The final answer was 116.

Example 7. Subtract 91899 from 100000

Subtract one from 100000, we get 99999

Now subtract 91899 from 99999

To the result 8100 we add one, which we subtracted from 100000

We received the final answer 8101.

The second way to subtract is to treat the digit in the digit as a number in its own right. Let's solve a few examples this way.

Example 8. Subtract 36 from 75

So, in the units place of the number 75 there is the number 5, and in the units place of the number 36 there is the number 6. You cannot subtract six from five, so we take one unit from the next number, which is in the tens place.

In the tens place there is the number 7. Take one unit from this number and mentally add it to the left of the number 5

And since one unit is taken from the number 7, this number will decrease by one unit and turn into the number 6

Now in the ones place of the number 75 there is the number 15, and in the ones place of the number 36 the number 6. From 15 you can subtract 6, you get 9. We write the number 9 in the ones place of the new number:

Let's move on to the next number, which is in the tens place. Previously, the number 7 was located there, but we took one unit from this number, so now the number 6 is located there. And in the tens place of the number 36 there is the number 3. From 6 you can subtract 3, you get 3. We write the number 3 in the tens place of the new number:

Example 9. Subtract 84 from 200

So, in the ones place of the number 200 there is a zero, and in the ones place of the number 84 there is a four. You cannot subtract four from zero, so we take one unit from the next number in the tens place. But in the tens place there is also a zero. Zero cannot give us one. In this case, we take 20 as the next number.

We take one unit from the number 20 and mentally add it to the left of the zero located in the ones place. And since one unit is taken from the number 20, this number will turn into the number 19

Now the number 10 is in the ones place. Ten minus four equals six. We write the number 6 in the units place of the new number:

Let's move on to the next number, which is in the tens place. Previously, there was a zero there, but this zero, together with the next digit 2, formed the number 20, from which we took one unit. As a result, the number 20 turned into the number 19. It turns out that now the number 9 is located in the tens place of the number 200, and the number 8 is located in the tens place of the number 84. Nine minus eight equals one. We write the number 1 in the tens place of our answer:

Let's move on to the next number, which is in the hundreds place. Previously, the number 2 was located there, but we took this number, together with the number 0, as the number 20, from which we took one unit. As a result, the number 20 turned into the number 19. It turns out that now in the hundreds place of the number 200 there is the number 1, and in the number 84 the hundreds place is empty, so we transfer this unit to the new number:

This method at first seems complicated and makes no sense, but in fact it is the easiest. We will mainly use it when adding and subtracting numbers in a column.

Column addition

Column addition is a school operation that many people remember, but it doesn’t hurt to remember it again. Column addition occurs by digits - units are added with units, tens with tens, hundreds with hundreds, thousands with thousands.

Let's look at a few examples.

Example 1. Add 61 and 23.

First, write down the first number, and below it the second number so that the units and tens of the second number are under the units and tens of the first number. We connect all this with an addition sign (+) vertically:

Now we add the units of the first number with the units of the second number, and the tens of the first number with the tens of the second number:

We got 61 + 23 = 84.

Example 2. Add 108 and 60

Now we add the units of the first number with the units of the second number, the tens of the first number with the tens of the second number, the hundreds of the first number with the hundreds of the second number. But only the first number 108 has a hundred. In this case, the digit 1 from the hundreds place is added to the new number (our answer). As they said at school, “it’s being demolished”:

It can be seen that we have added the number 1 to our answer.

When it comes to addition, it makes no difference in what order you write the numbers. Our example could easily be written like this:

The first entry, where the number 108 was at the top, is more convenient for calculation. A person has the right to choose any entry, but one must remember that units must be written strictly under units, tens under tens, hundreds under hundreds. In other words, the following entries will be incorrect:

If suddenly, when adding the corresponding digits, you get a number that does not fit into the digit of the new number, then you need to write down one digit from the low-order digit and move the remaining one to the next digit.

In this case, we are talking about the overflow of the discharge, which we talked about earlier. For example, when you add 26 and 98, you get 124. Let's see how it turned out.

Write the numbers in a column. Units under units, tens under tens:

Add the units of the first number with the units of the second number: 6+8=14. We received the number 14, which does not fit into the units category of our answer. In such cases, we first take out the digit from 14 that is in the ones place and write it in the units place of our answer. In the units place of the number 14 there is the number 4. We write this number in the units place of our answer:

Where should I put the number 1 from the number 14? This is where the fun begins. We transfer this unit to the next category. It will be added to the dozens of our answer.

Adding tens with tens. 2 plus 9 equals 11, plus we add the unit that we got from the number 14. By adding our unit to 11, we get the number 12, which we write in the tens place of our answer. Since this is the end of the solution, there is no longer a question of whether the resulting answer will fit into the tens place. We write down 12 in its entirety, forming the final answer.

We received a response of 124.

Using the traditional addition method, adding 6 and 8 units together results in 14 units. 14 units is 4 units and 1 ten. We wrote down four ones in the ones place, and sent one ten to the next place (to the tens place). Then, adding 2 tens and 9 tens, we got 11 tens, plus we added 1 ten, which remained when adding ones. As a result, we got 12 tens. We wrote down these twelve tens in their entirety, forming the final answer 124.

This simple example demonstrates a school situation in which they say “we write four, one in mind” . If you solve examples and after adding the digits you still have a number that you need to keep in mind, write it down above the digit where it will be added later. This will allow you not to forget about it:

Example 2. Add the numbers 784 and 548

Write the numbers in a column. Units under units, tens under tens, hundreds under hundreds:

Add the units of the first number with the units of the second number: 4+8=12. The number 12 does not fit into the units category of our answer, so we take out the number 2 from 12 from the ones category and write it into the units category of our answer. And we move the number 1 to the next digit:

Now we add up the tens. We add 8 and 4 plus the unit that remained from the previous operation (the unit remained from 12, in the figure it is highlighted in blue). Add 8+4+1=13. The number 13 will not fit into the tens place of our answer, so we write the number 3 in the tens place, and move the unit to the next place:

Now we add up the hundreds. We add 7 and 5 plus the unit that remains from the previous operation: 7+5+1=13. Write the number 13 in the hundreds place:

Column subtraction

Example 1. Subtract the number 53 from the number 69.

Let's write the numbers in a column. Units under units, tens under tens. Then we subtract by digits. From the units of the first number, subtract the units of the second number. From the tens of the first number, subtract the tens of the second number:

We received a response of 16.

Example 2. Find the value of the expression 95 − 26

The ones place of the number 95 contains 5 ones, and the ones place of the number 26 contains 6 ones. You cannot subtract six ones from five units, so we take one ten from the tens place. This ten and the existing five ones together make 15 units. From 15 units you can subtract 6 units to get 9 units. We write the number 9 in the units place of our answer:

Now let's subtract the tens. The tens place of 95 used to contain 9 tens, but we took one ten from that place, and now it contains 8 tens. And the tens place of the number 26 contains 2 tens. You can subtract two tens from eight tens to get six tens. We write the number 6 in the tens place of our answer:

Let's use it in which each digit included in a number is considered as a separate number. When subtracting large numbers into a column, this method is very convenient.

In the units place of the minuend is the number 5. And in the units place of the subtrahend is the number 6. You cannot subtract a six from a five. Therefore, we take one unit from the number 9. The taken unit is mentally added to the left of the five. And since we took one unit from the number 9, this number will decrease by one unit:

As a result, the five turns into the number 15. Now we can subtract 6 from 15. We get 9. We write the number 9 in the units place of our answer:

Let's move on to the tens category. Previously, the number 9 was located there, but since we took one unit from it, it turned into the number 8. In the tens place of the second number there is the number 2. Eight minus two is six. We write the number 6 in the tens place of our answer:

Example 3. Let's find the value of the expression 2412 − 2317

We write this expression in the column:

In the ones place of the number 2412 there is the number 2, and in the ones place of the number 2317 there is the number 7. You cannot subtract seven from two, so we take one from the next number 1. We mentally add the taken one to the left of the two:

As a result, two turns into the number 12. Now we can subtract 7 from 12. We get 5. We write the number 5 in the units place of our answer:

Let's move on to tens. In the tens place of the number 2412 there used to be the number 1, but since we took one unit from it, it turned into 0. And in the tens place of the number 2317 there is the number 1. You cannot subtract one from zero. Therefore, we take one unit from the next number 4. We mentally add the taken unit to the left of zero. And since we took one unit from the number 4, this number will decrease by one unit:

As a result, zero turns into the number 10. Now you can subtract 1 from 10. You get 9. We write the number 9 in the tens place of our answer:

In the hundreds place of the number 2412 there used to be a number 4, but now there is a number 3. In the hundreds place of the number 2317 there is also a number 3. Three minus three equals zero. The same goes for the thousand places in both numbers. Two minus two equals zero. And if the difference between the most significant digits is zero, then this zero is not written down. Therefore, the final answer will be the number 95.

Example 4. Find the value of the expression 600 − 8

In the units place of the number 600 there is a zero, and in the units place of the number 8 this number itself is located. You can’t subtract eight from zero, so we take one from the next number. But the next number is also zero. Then we take the number 60 as the next number. We take one unit from this number and mentally add it to the left of zero. And since we took one unit from the number 60, this number will decrease by one unit:

Now the number 10 is in the ones place. From 10 you can subtract 8, you get 2. Write the number 2 in the units place of the new number:

Let's move on to the next number, which is in the tens place. There used to be a zero in the tens place, but now there is a number 9 there, and in the second number there is no tens place. Therefore, the number 9 is transferred, as it is, to the new number:

Let's move on to the next number, which is in the hundreds place. There used to be a number 6 in the hundreds place, but now there is a number 5 there, and in the second number there is no hundreds place. Therefore, the number 5 is transferred, as it is, to the new number:

Example 5. Find the value of the expression 10000 − 999

Let's write this expression in a column:

In the units place of the number 10000 there is a 0, and in the units place of the number 999 there is a number 9. You cannot subtract nine from zero, so we take one unit from the next number, which is in the tens place. But the next digit is also zero. Then we take 1000 as the next number and take one from this number:

The next number in this case was 1000. Taking one from it, we turned it into the number 999. And we added the taken unit to the left of zero.

Further calculations were not difficult. Ten minus nine equals one. Subtracting the numbers in the tens place of both numbers gave zero. Subtracting the numbers in the hundreds place of both numbers also gave zero. And the nine from the thousands place was moved to a new number:

Example 6. Find the value of the expression 12301 − 9046

Let's write this expression in a column:

In the units place of the number 12301 there is the number 1, and in the units place of the number 9046 there is the number 6. You cannot subtract six from one, so we take one unit from the next number, which is in the tens place. But in the next digit there is a zero. Zero can't give us anything. Then we take 1230 as the next number and take one from this number:

Because decimal number system place number, then the number depends not only on the digits written in it, but also on the place where each digit is written.

Definition: The place where a digit is written in a number is called the digit of the number.

For example, a number consists of three digits: 1, 0 and 3. The place, or digit, notation system allows you to create three-digit numbers from these three digits: 103, 130, 301, 310 and two-digit numbers: 013, 031. The given numbers are arranged in order Ascending: every previous number less subsequent.

Consequently, the numbers that are used to write a number do not completely define this number, but only serve as a tool for writing it.

The number itself is constructed taking into account ranks, in which this or that digit is written, i.e., the desired digit must also occupy the desired place in the recording of the number.

Rule. Rank natural numbers are named from right to left from 1 to the larger number, each digit has its own number and place in the number record.

The most commonly used numbers have up to 12 digits. Numbers with more than 12 digits belong to the group of large numbers.

The number of places occupied by digits, provided that the largest digit is not 0, determines the digit capacity of the number. We can say about a number that it is: single-digit (single-digit), for example 5; two-digit (two-digit), for example 15; three-digit (three-digit), for example 551, etc.

In addition to the serial number, each of the digits has its own name: the units digit (1st), the tens digit (2nd), the hundreds digit (3rd), the units of thousands digit (4th), the tens of thousands digit (5th ) etc. Every three digits, starting from the first, are combined into classes. Every Class also has its own serial number and name.

For example, the first 3 category(from 1st to 3rd inclusive) - this is Class units with serial number 1; third Class- This Class million, it includes the 7th, 8th and 9th ranks.

Let us present the structure of the digit construction of a number, or a table of digits and classes.

The number 127 432 706 408 is twelve-digit and reads like this: one hundred twenty-seven billion four hundred thirty-two million seven hundred six thousand four hundred eight. This is a fourth grade multi-digit number. The three digits of each class are read as three-digit numbers: one hundred twenty-seven, four hundred thirty-two, seven hundred six, four hundred eight. To each class of a three-digit number the name of the class is added: “billions”, “millions”, “thousands”.

For the class of units, the name is omitted (implying “units”).

Numbers from 5th grade and above are considered large numbers. Large numbers are used only in specific branches of Knowledge (astronomy, physics, electronics, etc.).

Let us give an introduction to the names of the classes from the fifth to the ninth: the units of the 5th class are trillions, the 6th class are quadrillions, the 7th class are quintillions, the 8th class are sextillions, the 9th class are septillions.

Discharge

Morphology: (no) what? discharge, what? rank, (see) what? discharge, how? discharge, about what? about the category; pl. What? ranks, (no) what? ranks, what? discharges, (see) what? ranks, how? discharges, about what? about ranks

Atelier of the highest level. | In the classification of sciences, work according to artificial intelligence transferred from the category of theoretical to the category of applied sciences.

2. When they say that something from the category something, then this means that some event, incident, etc. can be attributed to some stable type.

Her secret was one of those that women prefer to take with them to the grave.

3. If anything is done first class, then this means that someone arranges something with the best of possible ways.

Have a first-class wedding.

4. Discharge The level of someone's qualifications in any profession, specialty, sport, etc. is called.

Fifth class mechanic. | Raise the rank of an experienced employee. | Receive the highest rank. | Third junior category in fencing.

5. In mathematics discharge is the place that a digit occupies when writing a number.

Senior rank. | Zero value of the left digit. | Two decimal places.

bit adj.

[energy] noun, m., used infrequently

1. Discharge is called the transfer of energy by the battery to the consumer.

The battery is completely discharged. | Time, battery discharge rate.

2. Electric discharge called the instantaneous flow of current through a gaseous medium, which is accompanied by a flash and a loud sound.

Arc discharge. | Atmospheric, lightning discharges. | Lightning strike. | Powerful, strong discharge.

bit adj.

Discharge current.

Dictionary Russian language Dmitriev. D. V. Dmitriev. 2003.

Synonyms:

See what “discharge” is in other dictionaries:

Comes from the verb “to discharge” or from the verb “to thin out”, has many meanings in various areas. Contents 1 Division 2 Management 3 Physics ... Wikipedia

DISCHARGE- (1) battery mode, reverse (see) battery, determined by its electrical capacity and consisting of a long-term return of accumulated electrical energy when the payload (external circuit) is turned on. R. acidic should not be allowed... ... Big Polytechnic Encyclopedia

Ushakov's Explanatory Dictionary

1. Rank 1, category, male. 1. who what. Department, group, genus, category in some division of objects, phenomena that differ in one way or another. Plant category (bot.). “Your whole previous life has led you to the conclusion that people... ... Ushakov's Explanatory Dictionary

Row, layer, genus, breed, species, subspecies, division, order, analysis, family, group, variety, category, series, class, type, genre; party, order, sect, section, school. Wed. . .. See degree... Dictionary of Russian synonyms and similar expressions. under … Synonym dictionary

1. DISCHARGE, a; m. 1. Group, genus, category of which l. objects, people, phenomena that are similar to each other in one way or another. Belong to the category strong-willed people. To fall into the category of those letters that are not answered. Atelier of the highest level.... ... encyclopedic Dictionary