Reading and writing large natural numbers. Ranks for beginners

This lesson will help you gain an understanding of the topic "Reading multi-digit numbers", which is included in school course 4th grade mathematics. The teacher will talk about how to correctly read multi-digit numbers consisting of thousands, and how to write such numbers correctly using numbers.

Introduction, introduction to a new class - the class of thousands

If there are a lot of objects, then when counting, they use not only the counting units you know: ones, de-syat-ki, hundreds - but also larger ones, for example, you-sya-chi. You-sya-chi count in the same way as simple ones: one you-sya-cha, two you-sya-chi, three you-sya-chi, four-you-re you-sya-chi and so on.

Ten thousand is one de-thousand thousand.

De-syat de-syat-kov thousand is one hundred thousand.

De-syat hundreds of thousands is you-sya-cha of thousands, or million-li-he.

So-sta-wim table of classes and ranks (Fig. 1).

Rice. 1. Table of classes and ranks

You know that one, de-syat-ki, hundreds make up the class of units, or the first class. Units of thousands, tens of thousands and hundreds of thousands make up the class of thousands, or the second class. Look at the table again: how many times in each class? Check it out: three times. Rows of the first class: single, de-syat-ki, hundreds. Rows of the second class: single thousands, de-syat-ki thousands and hundreds of thousands.

To read a multi-digit number, it is divided into classes, counted from the right by three digits, then count how -to one unit of each class, on-chi-naya from the highest.

Example

Three zeros in for-pi-si in-ka-zy-va-yut from the existence of units of the first class. The name of the class of units is not pro-of-but-sit-sya. Chi-ta-eat a number from the highest class: “three-hundred seven-de-syat two thousand-sya-chi.”

In this number, we see 145 units of the second class and 312 units of the first class. Chi-ta-em number from the highest class: "one hundred and forty-five thousand three-hundred and two-twenty."

This number includes 528 units of the second class and 609 units of the first class. Chi-ta-em number: "five-hundred twenty-twenty-seven thousand six-hundred de-syat."

In this number, there are 60 units of the second class and 500 units of the first class. This is "six-st-de-syat thousand five-hundred."

In the last number there are 7 units of the second class and 4 units of the first class. The number "seven thousand four-you-re."

Exercise 1

Break the number into classes. Tell me how many units of each class are in it.

From-count to the right of each number there are three digits.

Among 5 units of the second class and 400 units of the first class. Chi-ta-em: "five thousand che-you-re-hundred."

Among 5 units of the second class and 432 units of the first class. Chi-ta-em: “five thousand four-you-re-one hundred thirty-two.”

Among 61 units of the second class and 209 units of the first class. Chi-ta-em: "six-st-de-syat one you-sya-cha two-hundred de-vyat."

Among 61 units of the second class and 290 units of the first class. Chi-ta-em: "six-st-de-syat one you-sya-cha two-hundred de-vya-no-hundred."

Among 500 units of the second class and 500 units of the first class. Chi-ta-em: "five-hundred thousand five-hundred."

Among 500 units of the second class and 5 units of the first class. Chi-ta-em: "five-hundred thousand five."

Task 2

For-pi-shi-te digits-ra-mi numbers:

1. One hundred seven thousand three hundred nine

2. Thirty thousand seven hundred de nine

3. Seven thousand six hundred

Solution

Many-digit numbers for-pi-sy-va-yut by class, on-chi-naya from the highest. In order to write down numbers, for example, “one hundred eight thousand three hundred de-vyat”, sleep-cha-la for-pi-sy-va-yut, how many total units of the second, highest, class in number - 108, then for-pi-sy-va-yut, how many units of the first class in list.

For the number “thirty thousand seven-hundred seven-de-syat”, write down the number of units of the second highest class in the number, their three to give, and the number of units of the first class in number, seven hundred seven de syat.

Among the “seven thousand six hundred” there are 8 units of the second class and six hundred units of the first class.

Task 3

Pro-chi-tai-te in a different way: 3754, 2900, 3970.

Solution

3754. This number can be read differently:

A) 3 thousand 754 units.

The name of the class of units is usually not about-from-but-sit-sya, that’s why we pro-chi-ta-eat like this: three thou-sya-chi seven-hundred five- de-syat che-you-re.

B) 3 thousand 7 hundred. 5 dec. 4 units

We called the number of units of each-to-the-th time-series-yes.

C) 37 hundred. 5 dec. 4 units

D) 37 hundred. 54 units

D) 375 dec. 4 units

E) 3 thousand 75 dec. 4 units

A) 2 thousand 9 hundred.

B) 2 thousand 90 dess.

A) 3 thousand 9 hundred. 7 dec.

B) 3 thousand 97 dec.

C) 3 thousand 9 hundred. 70 units

D) 39 hundred. 7 dec.

D) 39 cells. 70 units

Property

A number in which there are units of different rows of rows can be replaced by the sum of my rows of weakly.

Task 4

For-me-no-those sum-my times-row-th sl-ha-e-my numbers:

1903: 1 thousand 9 hundred. 3 units

407 020: 4 cells. thousand 0 dec. thousand 7 units thousand 0 cells 2 dec. 0 units

300 206: 3 hundred. thousand 0 dec. thousand 0 units thousand 2 hundred. 0 dec. 6 units

164 800: 1 hundred. thousand 6 dec. thousand 4 units thousand 8 hundred. 0 dec. 0 units

Note: if there is zero in the row, you can not write it, because when adding zero, the same number is the same number.

If a natural number consists of one character - one digit, then it is called single-digit, for example, the numbers 3, 5, 9 are single-digit.

If a number consists of two characters - two digits, then it is called two-digit. For example, the numbers 10, 23, 75 are double digits.

Also, according to the number of characters in a given number, names are given to other numbers. For example: 145, 809 are three digit numbers.

There are four-digit numbers, five-digit numbers, and so on.

For reading, a multi-digit natural number is divided from right to left into groups of three digits each (the leftmost group can consist of one or two digits). These groups are called classes. Each of the three digits of the class denotes a digit: units digit, tens digit, hundreds digit.

The classification starts on the right. The first three digits on the right make up the class of units, the next three - the class of thousands, then comes the class of millions, then - billions. (see Fig.). Since the row natural numbers is infinite, then trillions follow billions, trillions follow trillions, and so on.

A million is a thousand thousand and is written with a one followed by six zeros.

A billion is a thousand million. It is written with a one followed by 9 zeros.

How to read a multi-digit number correctly? They begin to read a multi-digit number from left to right, in turn call the number of units of each class and add the name of the class. At the same time, the name of the class of units is not called, as well as the class in which all three digits are zeros.

For example, this number (42 135 308) is divided into classes as follows: it has 308 units, 135 units in the thousands class, 42 units in the millions class. Therefore, they read it like this: 42 million 135 thousand 308.

Any natural number can be represented as a sum of bit units.

For example:

32 537 = 30 000 + 2 000 + 500 + 30 + 7

Thus, in this lesson you got acquainted with the concept of a natural number and a natural series, learned to read and classify natural multi-digit numbers, as well as decompose them into categories.

Abstract source:: http://interneturok.ru/ru/school/matematika/4-klass/tema-3/chtenie-mnogoznachnyh-chisel?konspekt

http://znaika.ru/catalog/5-klass/matematika/Naturalnye-chisla.-Chtenie-i-zapis

Video source: http://www.youtube.com/watch?v=frHwo0rvmvM

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

The first class on the right is called unit class, second - thousand, third - million, fourth - billion, fifth - trillion, sixth - quadrillion, seventh - quintillion, eighth - sextillions.

For the convenience of reading the entry of a multi-digit number, a small gap is left between the classes. For example, to read the number 148951784296, we select classes in it:

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

148 billion 951 million 784 thousand 296.

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

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

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

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

All units except simple units are called constituent units. So, a dozen, a hundred, a thousand, etc. are constituent units. Every 10 units of any rank is one unit of the next (higher) rank. For example, a hundred contains 10 tens, a dozen - 10 simple ones.

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

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

For example, you want to know how many hundreds are in the number 6284, i.e. how many hundreds are in thousands and hundreds of this number together.

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

The number 0 in any category means the absence of units in this category. For example, the number 0 in the tens place means the absence of tens, in the hundreds place - the absence of hundreds, etc. In the place where 0 stands, nothing is pronounced when reading the number:

172 526 - one hundred seventy-two thousand five hundred twenty-six.
102026 - one hundred two thousand twenty-six.

Integers- natural numbers are numbers that are used to count objects. The set of all natural numbers is sometimes called the natural series: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, etc.

To write natural numbers, ten digits are used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. With the help of them, you can write any natural number. This notation is called decimal.

The natural series of numbers can be continued indefinitely. There is no number that would be the last one, because one can always be added to the last number and one will get a number that is already greater than the desired one. In this case, we say that there is no greatest number in the natural series.

Digits of natural numbers

In writing any number using numbers, the place on which the number stands in the number is crucial. For example, the number 3 means: 3 units if it comes last in the number; 3 tens if it will be in the number in the penultimate place; 4 hundreds, if she will be in the number in third place from the end.

The last digit means the units digit, the penultimate one - the tens digit, 3 from the end - the hundreds digit.

Single and multiple digits

If there is a 0 in any digit of the number, this means that there are no units in this digit.

The number 0 stands for zero. Zero is "none".

Zero is not a natural number. Although some mathematicians think otherwise.

If a number consists of one digit, it is called single-digit, two - two-digit, three - three-digit, etc.

Numbers that are not single digits are also called multiple digits.

Digit classes for reading large natural numbers

To read large natural numbers, the number is divided into groups of three digits, starting from the right edge. These groups are called classes.

The first three digits from the right edge make up the units class, the next three the thousands class, the next three the millions class.

A million is a thousand thousand, for the record they use the abbreviation million 1 million = 1,000,000.

A billion = a thousand million. For recording, the abbreviation billion 1 billion = 1,000,000,000 is used.

Write and Read Example

This number has 15 units in the billions class, 389 units in the millions class, zero units in the thousands class, and 286 units in the units class.

This number reads like this: 15 billion 389 million 286.

Read numbers from left to right. In turn, the number of units of each class is called and then the name of the class is added.

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

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

The symbols used to write numbers are called figures .

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

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

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

Bit units

Notation which we use is called decimal. Because it is exactly ten units of one category that makes up one unit of the next category.

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

10 ones - 1 ten (10)

10 tens - 1 hundred (100)

10 hundreds - 1 thousand (1000)

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

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

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

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

We talked about the fact that 0 is an insignificant number, which means the absence of something. In numbers, the number 0 means the absence of ones in the discharge.

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

And the numbers in the digits of which there are no zeros are called complete .

The digits are counted from right to left:

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

1. In list 2375 :

5 units of the first category, or 5 units

7 units of the second digit, or 7 tens

3 units of the third category, or 3 hundreds

2 units of the fourth category, or 2 thousand

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

1. In list 1000462086432

2 pieces

3 dozen

8 tens of thousands

0 hundred thousand

2 units million

6 tens of millions

4 hundred million

0 units billion

0 tens of billions

0 hundred billion

1 unit trillion

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

1. In list 83 :

3 units

8 tens

Pronounced like this: eighty three .

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

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

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

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

For example, number 6734 can be represented like this:

6000 + 700 + 30 + 4 = 6734