Difference of bit terms. The sum of the digit terms of a natural number

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 number. Another example single digit numbers: 3, 5, 8.
67 consists of two digits, so this number is called double digit number. Example double 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 there are tens given number No.
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 sextillions.

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 amount 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

To record numbers, people came up with ten characters called numbers. These are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

You can write any natural number using ten digits.

Its name depends on the number of characters (digits) in a number.

A number consisting of one sign (digit) is called single-digit. The smallest single-digit natural number is 1, the largest is 9.

A number consisting of two characters (digits) is called two-digit. The smallest two-digit number is 10, the largest is 99.

Numbers written with two, three, four or more digits are called two-digit, three-digit, four-digit or multi-digit numbers. Least three-digit number- 100, highest - 999.

Each digit in the entry multi-digit number occupies a certain place - position.

Discharge- this is the place (position) where the digit appears in the notation of a number.

The same digit in a number may have different meanings depending on what category it is in.

Places are counted from the end of the number.

Units digit is the least significant digit that ends any number.

The number 5 means 5 units if the five is on last place in the notation of numbers (in the units place).

Tens place is the digit that comes before the units digit.

The number 5 means 5 tens if it is in the penultimate place (in the tens place).

Hundreds place is the digit that comes before the tens digit. The number 5 means 5 hundreds if it is in third place from the end of the number (in the hundreds place).

If a number is missing any digit, then the number will be written in its place with the number 0 (zero).

Example. The number 807 contains 8 hundreds, 0 tens and 7 units - this notation is called digit composition of the number.

807 = 8 hundreds 0 tens 7 units

Every 10 units of any rank form a new unit of a higher rank. For example, 10 ones make 1 ten, and 10 tens make 1 hundred.

Thus, the value of a digit from digit to digit (from units to tens, from tens to hundreds) increases 10 times. Therefore, the counting system we use is called the decimal number system.

Classes and ranks

In the notation of a number, the digits, starting from the right, are grouped into classes of three digits each.

Unit class or the first class is the class formed by the first three digits (to the right of the end of the number): units place, tens place and hundreds place.

www.mamapapa-arh.ru

Place numbers

Sum of bit terms

Any natural number can be written as a sum of digit terms.

How this is done can be seen from the following example: the number 999 consists of 9 hundreds, 9 tens and 9 units, therefore:

999 = 9 hundreds + 9 tens + 9 ones = 900 + 90 + 9

The numbers 900, 90 and 9 are digit terms. Bit term is simply the number of ones in a given digit.

The sum of the bit terms can also be written as follows:

999 = 9 100 + 9 10 + 9 1

The numbers by which multiplication is performed (1, 10, 100, 1000, etc.) are called digit units. So, 1 is the unit of the units place, 10 is the unit of the tens place, 100 is the unit of the hundreds place, etc. Numbers that are multiplied by the place units express number of digit units.

Write any number in the form:

12 = 1 10 + 2 1 or 12 = 10 + 2

called decomposition of a number into digit terms(or sum of bit terms).

3278 = 3 1000 + 2 100 + 7 10 + 8 1 = 3000 + 200 + 70 + 8
5031 = 5 1000 + 0 100 + 3 10 + 1 1 = 5000 + 30 + 1
3700 = 3 1000 + 7 100 + 0 10 + 0 1 = 3000 + 700

Calculator for decomposing a number into digit terms

This calculator will help you represent a number as a sum of digit terms. Just enter the desired number and click the Expand button.

Place terms in mathematics

A number is a mathematical concept for a quantitative description of something or its part; it also serves to compare the whole and parts, and arrange them in order. The concept of number is represented by signs or numbers in various combinations. Currently, numbers from 1 to 9 and 0 are used almost everywhere. Numbers in the form of seven Latin letters have almost no application and will not be considered here.

Integers

When counting: “one, two, three... forty-four” or arranging in order: “first, second, third... forty-four,” natural numbers are used, which are called natural numbers. This entire set is called the “series of natural numbers” and is denoted Latin letter N has no end, because there is always an even larger number, and the largest one simply does not exist.

Places and classes of numbers

This shows that the digit of a number is its position in digital notation, and any value can be represented through digit terms in the form nnn = n00 + n0 + n, where n is any digit from 0 to 9.

One ten is a unit of the second digit, and one hundred is a unit of the third. Units of the first category are called simple, all others are composite.

For ease of recording and transmission, categories are grouped into classes of three in each. It is allowed to put a space between classes for ease of reading.

First - units, contains up to 3 characters:

Two hundred and thirteen contains the following bit terms: two hundred, one ten and three prime ones.

Forty-five is made up of four tens and five prime units.

Second - thousand, from 4 to 6 characters:

• 679 812 = 600 000 + 70 000 + 9 000 + 800 +10 + 2.

This sum consists of the following bit terms:

1. six hundred thousand;
2. seventy thousand;
3. nine thousand;
4. eight hundred;
5. ten;

• 3 456 = 3000 + 400 +50 +6.

There are no terms above the fourth digit.

Third - millions, from 7 to 9 digits:

This number contains nine digit terms:

1. 800 million;
2. 80 million;
3. 7 million;
4. 200 thousand;
5. 10 thousand;
6. 3 thousand;
7. 6 hundreds;
8. 4 tens;
9. 4 units;

• 7 891 234.

There are no terms in this number above the 7th digit.

The fourth is billions, from 10 to 12 digits:

Five hundred sixty-seven billion eight hundred ninety-two million two hundred thirty-four thousand nine hundred seventy-six.

Class 4 bit terms are read from left to right:

1. units of hundreds of billions;
2. units of tens of billions;
3. units of billions;
4. hundreds of millions;
5. tens of millions;
6. millions;
7. hundreds of thousands;
8. tens of thousands;
9. thousand;
10. simple hundreds;
11. simple tens;
12. simple units.

The digit of a number is numbered starting from the smallest, and reading - from the largest.

If there are no intermediate values ​​in the number of terms, zeros are placed when writing; when pronouncing the name of the missing digits, as well as the class of units, the name is not pronounced:

Four hundred billion four. The following names of categories are not pronounced here due to absence: tenth and eleventh fourth grade; ninth, eighth and seventh third and most? third class; the names of the second class and its ranks, as well as hundreds and tens of units, are also not announced.

The fifth is trillions, from 13 to 15 characters.

Four hundred eighty-seven trillion seven hundred eighty-nine billion six hundred fifty-four million four hundred twenty-seven two hundred forty-one.

The sixth is quadrillion, 16-18 digits.

• 321 546 818 492 395 953;

Three hundred twenty-one quadrillion five hundred forty-six trillion eight hundred eighteen billion four hundred ninety-two million three hundred ninety-five thousand nine hundred fifty-three.

Seventh - quintillion, 19-21 digits.

• 771 642 962 921 398 634 389.

Seven hundred seventy-one quintillion six hundred forty-two quadrillion nine hundred sixty-two trillion nine hundred twenty-one billion three hundred ninety-eight million six hundred thirty-four thousand three hundred eighty-nine.

Eighth - sextillion, 22-24 digits.

• 842 527 342 458 752 468 359 173

Eight hundred and forty-two sextillion, five hundred and twenty-seven quintillion, three hundred and forty-two quadrillion, four hundred and fifty-eight trillion, seven hundred and fifty-two billion, four hundred and sixty-eight million, three hundred and fifty-nine thousand, one hundred and seventy-three.

You can simply distinguish classes by numbering, for example, the number of class 11 contains from 31 to 33 characters when written.

But in practice, writing such a number of characters is inconvenient and most often leads to errors. Therefore, when performing operations with such quantities, the number of zeros is reduced by raising them to a power. After all, it is much easier to write 10 31 than to add thirty-one zeros to one.

education.guru

What are bit terms?

Answers and explanations

For example: 5679=5000+600+70+9
That is, the number of units in the category

• Comments (1)
• Flag violation

the sum of the digit terms of the number 526 is 500+20+6

“sum of digit terms” is a representation of a two (or more) digit number as the sum of its digits.

Place terms are the addition of numbers with different bit depths. For example, we divide the number 17.890 into digit terms: 17.890=10.000+7.000+800+90+0

Rule for multiplying any number by zero

Even at school, teachers tried to hammer into our heads the simplest rule: “Any number multiplied by zero equals zero!”, – but still a lot of controversy constantly arises around him. Some people just remember the rule and don’t bother themselves with the question “why?” “You can’t and that’s it, because they said so at school, the rule is the rule!” Someone can fill half a notebook with formulas, proving this rule or, conversely, its illogicality.

Who's right in the end?

During these disputes, both people with opposing points of view look at each other like a ram and prove with all their might that they are right. Although, if you look at them from the side, you can see not one, but two rams, resting their horns on each other. The only difference between them is that one is slightly less educated than the other. Most often, those who consider this rule to be incorrect try to appeal to logic in this way:

I have two apples on my table, if I put zero apples on them, that is, I don’t put a single one, then my two apples will not disappear! The rule is illogical!

Indeed, apples will not disappear anywhere, but not because the rule is illogical, but because a slightly different equation is used here: 2 + 0 = 2. So let’s discard this conclusion right away - it is illogical, although it has the opposite goal - to call to logic.

This is interesting: How to find the difference between numbers in mathematics?

What is multiplication

Originally the multiplication rule was defined only for natural numbers: multiplication is a number added to itself a certain number of times, which implies that the number is natural. Thus, any number with multiplication can be reduced to this equation:

1. 25?3 = 75
2. 25 + 25 + 25 = 75
3. 25?3 = 25 + 25 + 25

From this equation it follows that that multiplication is a simplified addition.

What is zero

Any person knows from childhood: zero is emptiness. Despite the fact that this emptiness has a designation, it does not carry anything at all. Ancient Eastern scientists thought differently - they approached the issue philosophically and drew some parallels between emptiness and infinity and saw deep meaning in this number. After all, zero, which has the meaning of emptiness, standing next to any natural number, multiplies it ten times. Hence all the controversy about multiplication - this number carries so much inconsistency that it becomes difficult not to get confused. In addition, zero is constantly used to define empty digits in decimals, this is done both before and after the decimal point.

Is it possible to multiply by emptiness?

It is possible to multiply by zero, but it is useless, because, whatever one may say, even when multiplying negative numbers it will still be zero. It’s enough just to remember this simple rule and never ask this question again. In fact, everything is simpler than it seems at first glance. There are no hidden meanings and secrets, as ancient scientists believed. Below we will give the most logical explanation that this multiplication is useless, because when you multiply a number by it, you will still get the same thing - zero.

Returning to the very beginning, to the argument about two apples, 2 times 0 looks like this:

• If you eat two apples five times, then you eat 2?5 = 2+2+2+2+2 = 10 apples
• If you eat two of them three times, then you eat 2?3 = 2+2+2 = 6 apples
• If you eat two apples zero times, then nothing will be eaten - 2?0 = 0?2 = 0+0 = 0

After all, eating an apple 0 times means not eating a single one. It will be clear even to yourself to a small child. Whatever one may say, the result will be 0, two or three can be replaced with absolutely any number and the result will be absolutely the same. And to put it simply, then zero is nothing, and when do you have there is nothing, then no matter how much you multiply, it’s still the same will be zero. There is no such thing as magic, and nothing will make an apple, even if you multiply 0 by a million. This is the simplest, most understandable and logical explanation of the rule of multiplication by zero. For a person who is far from all formulas and mathematics, such an explanation will be enough for the dissonance in the head to resolve and everything to fall into place.

From all of the above, another important rule follows:

You can't divide by zero!

This rule has also been persistently hammered into our heads since childhood. We just know that it’s impossible to do everything without filling our heads with unnecessary information. If you are unexpectedly asked the question why it is forbidden to divide by zero, then the majority will be confused and will not be able to clearly answer the simplest question from school curriculum, because there is not so much controversy and controversy surrounding this rule.

Everyone simply memorized the rule and did not divide by zero, not suspecting that the answer was hidden on the surface. Addition, multiplication, division and subtraction are unequal; of the above, only multiplication and addition are valid, and all other manipulations with numbers are built from them. That is, the entry 10: 2 is an abbreviation of the equation 2 * x = 10. This means that the entry 10: 0 is the same abbreviation for 0 * x = 10. It turns out that division by zero is a task to find a number, multiplying by 0, you get 10 And we have already figured out that such a number does not exist, which means that this equation has no solution, and it will be a priori incorrect.

Let me tell you,

So as not to divide by 0!

Cut 1 as you want, lengthwise,

Just don't divide by 0!

education.guru

• Sailing ships Types of sailing ships Depending on the sailing rig carried (straight, oblique, mixed) and the number of masts, sailing ships have the following names (Fig. 44): ships with direct sails - ship, brig, with oblique sails: single-masted - sloop , tender; one and a half mast - ketch, iol; […]
• Criminal law course. A common part. Volume 1. The doctrine of crime See Course in criminal law. General part: Volume 1, Volume 2, Special part: Volume 3, Volume 4, Volume 5 Chapter I. Concept, subject, method, system, tasks of criminal law _ 1. Subject and concept of criminal law _ 2. Methods of criminal law _ 3 . Tasks […]
• Law of Muna The Laws of Manu are an ancient Indian collection of instructions for religious, moral and social duty (dharma), also called the “law of the Aryans” or the “code of honor of the Aryans.” Manavadharmasastra is one of the twenty Dharmasastras. Here are selected fragments (translation by Georgy Fedorovich […]
• Basic ideas and concepts necessary for organizing volunteer (voluntary) activities. 1. General approaches to organizing volunteer (volunteer) activities. 1.1.Basic ideas and concepts necessary for organizing volunteer (voluntary) activities. 1.2. Legislative framework for volunteer […]
• Kashin is a lawyer for lawyers included in the register of lawyers of the Tver region Branch No. 1 TOKA (Tver, Sovetskaya St., 51; t.t. 33-20-55; 32-07-47; 33-20-63) Head of the branch - Strelkov Anatoly Vladimirovich) (d.t.42-61-44) 1. Duksova Maria Ivanovna – born 01/15/1925 2. Vladimir Evgenievich Dunaevsky – born November 25, 1953 […] Antipin VV lawyer All information provided is for informational purposes only and is not a public offer as defined by the provisions of Article 437 of the Civil Code of the Russian Federation. The information provided may no longer be relevant due to changes made. List of lawyers providing free legal […]

To perform some operations on natural numbers, you have to represent these natural numbers in the form sums of bit terms or, as they also say, sort natural numbers into digits. No less important is the reverse process - recording natural number by the sum of the bit terms.

In this article, we will use examples to understand in great detail the representation of natural numbers in the form of a sum of digit terms, and also learn how to write a natural number using its well-known digit decomposition.

Page navigation.

Representation of a natural number as a sum of digit terms.

As you can see, the title of the article contains the words “sum” and “addends”, so first we recommend that you have a good understanding of the information in the article, a general understanding of the addition of natural numbers. It also wouldn’t hurt to repeat the material from the section digit, the value of the digit of a natural number.

Let's take on faith the following statements that will help us define bit terms.

Place terms can only be natural numbers whose entries contain a single digit other than the number 0 . For example, natural numbers 5 , 10 , 400 , 20 000 and so on. can be digit terms, and numbers 14 , 201 , 5 500 , 15 321 and so on. - can not.

The number of digit terms of a given natural number must be equal to the number of digits in the recording of a given number other than the digit 0 . For example, a natural number 59 can be represented as a sum of two digit terms, since this number involves two digits ( 5 And 9 ), different from 0 . And the sum of the digit terms of a natural number 44 003 will consist of three terms, since the number record contains three digits 4 , 4 And 3 , which differ from the numbers 0 .

All bit terms of a given natural number in their notation contain a different number of characters.

The sum of the digit terms of a given natural number must be equal to the given number.

Now we can give a definition of bit terms.

Definition.

Bit terms of a given natural number are such natural numbers as

• in which there is only one digit other than the number 0 ;
• the number of which is equal to the number of digits in a given natural number other than the digit 0 ;
• whose records consist of a different number of characters;
• the sum of which is equal to a given natural number.

From the above definition it follows that single-digit natural numbers, as well as multi-digit natural numbers, the entries of which consist entirely of digits 0 , with the exception of the first digit on the left, do not decompose into the sum of digit terms, since they themselves are digit terms of some natural numbers. The remaining natural numbers can be represented as a sum of digit terms.

It remains to deal with the representation of natural numbers in the form of a sum of digit terms.

To do this, you need to remember that natural numbers are inherently related to the number of certain objects, while in writing a number, the values ​​of the digits set the corresponding quantities of units, tens, hundreds, thousands, tens of thousands, and so on. For example, a natural number 48 answers 4 dozens and 8 units, and the number 105 070 corresponds 1 a hundred thousand 5 thousands and 7 dozens. Then, due to the meaning of addition of natural numbers, the following equalities are true: 48=40+8 And 105 070=100 000+5 000+70 . This is how we represented natural numbers 48 And 105 070 in the form of a sum of bit terms.

Reasoning in a similar way, we can decompose any natural number into digits.

Let's give another example. Let's imagine a natural number 17 in the form of a sum of bit terms. Number 17 corresponds 1 ten and 7 units, therefore 17=10+7 . This is the decomposition of the number 17 by category.

And here is the amount 9+8 is not the sum of the digit terms of a natural number 17 , since in the sum of the bit terms there cannot be two numbers whose records consist of the same number of characters.

Now it has become clear why bit terms are called bit terms. This is due to the fact that each digit term is a “representative” of its digit of a given natural number.

Finding a natural number from a known sum of digit terms.

Let's consider the inverse problem. We will assume that we are given the sum of the digit terms of some natural number, and we need to find this number. To do this, you can imagine that each of the digit terms is written on a transparent film, but the areas with numbers other than 0 are not transparent. To obtain the desired natural number, you need to “superpose” all the bit terms on top of each other, matching their right edges.

For example, the amount 300+20+9 represents the expansion into digits of a number 329 , and the sum of bit terms of the form 2 000 000+30 000+3 000+400 corresponds to a natural number 2 033 400 . That is, 300+20+9=329 , A 2 000 000+30 000+3 000+400=2 033 400 .

To find a natural number by known amount digit terms, you can add these digit terms in a column (if necessary, refer to the material in the article adding natural numbers in a column). Let's look at the solution to the example.

Let's find a natural number if given the sum of the digit terms of the form 200 000+40 000+50+5 . Writing down the numbers 200 000 , 40 000 , 50 And 5 as required by the column addition method:

All that remains is to add the numbers in columns. To do this, you need to remember that the sum of zeros is equal to zero, and the sum of zeros and a natural number is equal to this natural number. We get

Under the horizontal line we got the required natural number 240 055 , the sum of the bit terms of which has the form 200 000+40 000+50+5 .

In conclusion, I would like to draw your attention to one more point. The skills of decomposing natural numbers into digits and the ability to perform the inverse operation allow one to represent natural numbers as a sum of terms that are not digits. For example, expansion into digits of a natural number 725 has the following form 725=700+20+5 , and the sum of the bit terms 700+20+5 due to the properties of addition of natural numbers, it can be represented as (700+20)+5=720+5 or 700+(20+5)=700+25, or (700+5)+20=705+20.

A logical question arises: “What is this for?” The answer is simple: in some cases it can simplify calculations. Let's give an example. Let's subtract natural numbers 5 677 And 670 . First, let's imagine the minuend as a sum of bit terms: 5 677=5 000+600+70+7 . It is easy to see that the resulting sum of bit terms is equal to the sum (5,000+7)+(600+70)=5,007+670. Then
5 677−670=(5 007+670)−670= 5 007+(670−670)=5 007+0=5 007 .

Bibliography.

• Mathematics. Any textbooks for 1st, 2nd, 3rd, 4th grades of general education institutions.
• Mathematics. Any textbooks for 5th grade of general education institutions.

Guys, open your textbook to page 24. Read the title of today's topic at the top.

Today we will learn what digit terms mean, and we will also learn to represent a number as a sum of digit terms. We complete task number 1. I read the task, you listen carefully. Write the numbers 18, 15, 19, 14 in your notebook.

The teacher writes these numbers on the board.

For each number, highlight the tens digit in red. What numbers will you highlight?

The teacher underlines the number 1 in red on the board.

In the same numbers, highlight the units digits in blue. What numbers will you highlight?

The teacher on the board underlines the number 8, 5, 9, 4 in blue in each number.

How are these numbers similar?

How are these numbers different?

Write each of these two-digit numbers as a sum whose first term is 10.

In what sum can the number 18 be given if this number consists of 1 ten and 8 units?

Now I will read how Masha presented the number 18. So, Masha presented the number 18 as the sum of 10+8. This representation of numbers is called So we correctly represented the number 18 as the sum of 10+8?

Divide the remaining numbers, 15, 19, 14, into place value terms. How will you present these numbers as a sum?

That's right guys, this representation of a number is called BY DECOMPOSITION INTO DIAGRAM COMPANDS. Write down these amounts in your notebook.

Task number 2. Write down the numbers 15, 16, 11, 10 in your notebook. Write these numbers in your notebook.

The teacher writes numbers on the board.

How many tens are in each of these numbers?

How many units are there in each number?

Represent each number as a sum of digit terms.

The teacher writes the amounts on the board.

Task number 3. Look at the pictures and write down the numbers. First picture, what number should we write down?

Second picture, what number should we write down?

The teacher writes the number on the board.

Third picture, what number should we write down?

The teacher writes the number on the board.

Fourth picture, what number should we write down?

The teacher writes the number on the board.

Fifth picture, what number should we write down?

The teacher writes the number on the board.

How many tens and how many ones are there in each of these numbers?

Write down a number that has 2 tens and 0 ones. What number is this?

The teacher writes the number 20 on the board.

That's right, that's the number TWENTY.

- How is the number 20 represented in the last picture?

Write down all the numbers from 11 to 20 in order.

The teacher writes numbers from 11 to 20 on the board.

So guys, all numbers from 11 to 20 are These are the numbers of the second ten.

And now we will have a physical minute.

A number is a mathematical concept for a quantitative description of something or its part; it also serves to compare the whole and parts, and arrange them in order. The concept of number is represented by signs or numbers in various combinations. Currently, numbers from 1 to 9 and 0 are used almost everywhere. Numbers in the form of seven Latin letters have almost no application and will not be considered here.

Integers

When counting: “one, two, three... forty-four” or arranging in order: “first, second, third... forty-four,” natural numbers are used, which are called natural numbers. This entire set is called a “series of natural numbers” and is denoted by the Latin letter N and has no end, because there is always an even larger number, and the largest one simply does not exist.

Places and classes of numbers

Rank

dozens

• 10…90;

• 100…900.

This shows that the digit of a number is its position in digital notation, and any value can be represented through digit terms in the form nnn = n00 + n0 + n, where n is any digit from 0 to 9.

One ten is a unit of the second digit, and one hundred is a unit of the third. Units of the first category are called simple, all others are composite.

For ease of recording and transmission, categories are grouped into classes of three in each. It is allowed to put a space between classes for ease of reading.

Classes

First - units, contains up to 3 characters:

• 200 + 10 +3 = 213.

Two hundred and thirteen contains the following bit terms: two hundred, one ten and three prime ones.

• 40 + 5 = 45;

Forty-five is made up of four tens and five prime units.

Second - thousand, from 4 to 6 characters:

• 679 812 = 600 000 + 70 000 + 9 000 + 800 +10 + 2.

This sum consists of the following bit terms:

1. six hundred thousand;
2. seventy thousand;
3. nine thousand;
4. eight hundred;
5. ten;

• 3 456 = 3000 + 400 +50 +6.

There are no terms above the fourth digit.

Third - millions, from 7 to 9 digits:

• 887 213 644;

This number contains nine digit terms:

1. 800 million;
2. 80 million;
3. 7 million;
4. 200 thousand;
5. 10 thousand;
6. 3 thousand;
7. 6 hundreds;
8. 4 tens;
9. 4 units;

• 7 891 234.

There are no terms in this number above the 7th digit.

The fourth is billions, from 10 to 12 digits:

• 567 892 234 976;

Five hundred sixty-seven billion eight hundred ninety-two million two hundred thirty-four thousand nine hundred seventy-six.

Class 4 bit terms are read from left to right:

1. units of hundreds of billions;
2. units of tens of billions;
3. units of billions;
4. hundreds of millions;
5. tens of millions;
6. millions;
7. hundreds of thousands;
8. tens of thousands;
9. thousand;
10. simple hundreds;
11. simple tens;
12. simple units.

The digit of a number is numbered starting from the smallest, and reading - from the largest.

If there are no intermediate values ​​in the number of terms, zeros are placed when writing; when pronouncing the name of the missing digits, as well as the class of units, the name is not pronounced:

• 400 000 000 004;

Four hundred billion four. The following names of categories are not pronounced here due to absence: tenth and eleventh fourth grade; ninth, eighth and seventh third and third grade itself; the names of the second class and its ranks, as well as hundreds and tens of units, are also not announced.

The fifth is trillions, from 13 to 15 characters.

• 487 789 654 427 241.

Reads on the left:

Four hundred eighty-seven trillion seven hundred eighty-nine billion six hundred fifty-four million four hundred twenty-seven two hundred forty-one.

The sixth is quadrillion, 16-18 digits.

• 321 546 818 492 395 953;

Three hundred twenty-one quadrillion five hundred forty-six trillion eight hundred eighteen billion four hundred ninety-two million three hundred ninety-five thousand nine hundred fifty-three.

Seventh - quintillion, 19-21 digits.

• 771 642 962 921 398 634 389.

Seven hundred seventy-one quintillion six hundred forty-two quadrillion nine hundred sixty-two trillion nine hundred twenty-one billion three hundred ninety-eight million six hundred thirty-four thousand three hundred eighty-nine.

Eighth - sextillion, 22-24 digits.

• 842 527 342 458 752 468 359 173

Eight hundred and forty-two sextillion, five hundred and twenty-seven quintillion, three hundred and forty-two quadrillion, four hundred and fifty-eight trillion, seven hundred and fifty-two billion, four hundred and sixty-eight million, three hundred and fifty-nine thousand, one hundred and seventy-three.

You can simply distinguish classes by numbering, for example, the number of class 11 contains from 31 to 33 characters when written.

But in practice, writing such a number of characters is inconvenient and most often leads to errors. Therefore, when performing operations with such quantities, the number of zeros is reduced by raising them to a power. After all, it is much easier to write 10 31 than to add thirty-one zeros to one.