Decimals. Presentation of the lesson: "Decimal fractions. Reading and writing decimal fractions" (Grade 5 Mathematics) Reading and writing decimal fractions
Numbers
mixed numbers
natural
Improper common fractions
Proper common fractions
NAME THE NATURAL NUMBERS
NAME mixed NUMBERS
NAME common fractions
What numbers are left?
FRACTIONAL NUMBERS IN
DECIMAL RECORD.
DECIMAL FRACTIONS.
TOPIC OF TODAY'S LESSON:
Decimals. Reading and writing decimals.
THE PURPOSE OF THE LESSON:
Introduce the concept of decimals. Learn to read and write decimals Learn to translate an ordinary fraction with denominators 10, 100, 1000, etc. to decimal and vice versa Develop logical thinking in a new situation Cultivate independence and responsibility for their own activities.
Fractions
Ordinary
Decimals, fractions
Decimals.
SIGN UP
READ
Decimals
ACTIONS
WITH DECIMAL
COMPARE
If a comma is used in the decimal notation of a number, then they say that the number is written as a decimal fraction.
Numbers with a denominator ten; 100; 1000 etc. agreed to write without a denominator
MATHEMATICAL DICTION
WRITE THE NUMBERS
- THREE POINT SEVEN TENTH
- SIX ONE Hundredth
- FIVE FOUR THOUSANDTHS
MATHEMATICAL DICTION
WRITE THE NUMBERS
First write the integer part, and then the numerator of the fractional part
The integer part is separated from the fractional part by a comma
Numbers with denominators 10, 100, 1000, etc.
agreed to write without a denominator
After the decimal point, the numerator of the fractional part must have as many digits as there are zeros in the denominator
ALGORITHM
1. WRITE THE INTEGER PART OF THE NUMBER
2. PUT A COMMA
3. PUT AS MANY POINTS AFTER THE COMMA AS THERE ARE ZEROS IN THE DENOMINATOR
4. FROM THE LAST POINT, WRITE THE NUMBER
5. WE REPLACE THE REMAINING POINTS WITH ZEROS
Decimals are made up of an integer part and a fractional
Digits of the integer part of the number
Fractional digits
thousandths
ten-thousandths
hundred-thousandths
millions
3
4
5
2
3
4
5
2
4
5
0
2
FIVE POINT THREE TENTH
TWENTY ONE POINT SEVEN Hundredths
THREE POINT SEVEN TENTH
TWO HUNDRED FIFTY SIX THOUSANDTHS
SEVEN POINT TWENTY NINE Hundredths
SIX ONE Hundredth
FIVE FOUR THOUSANDTHS
NINE POINT EIGHT TEN THOUSAND
= 9,0008
FIND AND WRITE THE MISSING NUMBERS
The origin and development of decimal fractions
Uzbekistan, XV century
Europe, 16th century
Russia, XVIII century
Ancient China, 2nd century BC
The origin and development of decimal fractions in China was closely connected with metrology (the study of measures). Already in the II century BC. there was a decimal system of measures of length.
AT 1427 year, mathematician
and an astronomer Uzbekistan ,
Al-Kashi wrote a book
"Key to Arithmetic"
in which he formulated
main
rules of action
with decimals
Uzbekistan, XV century
EUROPE,
century
AT 1579 decimal fractions are used in the "Mathematical Canon" by the French mathematician François Vieta (1540-1603), published in Paris.
wide
decimal spread
in Europe began only after the publication of the book "Tenth" by the Flemish mathematician Simon Stevin (1548-1620 ). He is considered the inventor of decimal fractions.
Russia, XVIII century
AT Russia first
systematic information
about decimals
found in "Arithmetic"
L.F. Magnitsky (1703)
2,135436
2 | 135436
Uzbekistan
France
Russia
Europe
1 cun
3 shares,
5 ordinal,
4 hairs,
3 thinnest,
6 cobwebs
2,135436
China
2 135436
2 0 1 1 3 2 5 3 4 4 3 5 6 6
Are you tired?
Well, then everyone stood up together.
We stretch our arms, shoulders,
To make it easier for us to sit.
And don't get tired.
check
Write the following fractions as decimals:
Write the following fractions as common fractions or as a mixed number:
Summarize:
- What fraction can replace an ordinary fraction, the denominator of the fractional part of which is expressed unit with one or a few zeros?
- What separates the integer part of a decimal fraction from
fractional part?
- If the fraction is correct, then what is written before
write a comma?
- How many digits must be after the decimal point in
decimal notation?
Homework
clause 7.1;
answer the questions
№ 1211,№1212
(on repeat #1216)
Subject: mathematics Grade: 5
Lesson topic: " Decimal. Reading and writing decimals.
Lesson Objectives:
educational: to study the concept of decimal fractions, to learn how to read and write decimal fractions, to form the ability to read and write decimal fractions;developing: develop logical thinking, the ability to analyze, compare, generalize, draw conclusions, develop attention;educational: to educate students in diligence, accuracy, skills of self-control, friendliness, mutual assistance.
Lesson type: learning new material.
Teaching methods: verbal, practical, individual.
Lesson plan:
1. Organizational moment.
2. Oral questioning.
3. Explanation of new material.
3. Consideration of examples, orally.
4. Consolidation of knowledge.
5. Grades for the lesson.
6. Statement of the task at home.
During the classes:
1. Organizing moment.
Hello guys! Sit down! (The journal is filled in, absent students are noted).
2. Oral questioning:
a) What fractions have we studied?
b) What are common fractions?
c) What operations on ordinary fractions can we perform?
Today in the lesson we will get acquainted with new fractions - decimals.
3. Learning new material.
Among ordinary fractions and mixed numbers, fractions with a denominator that is a multiple of 10 are often found. For example, if you express 9 mm in centimeters; 15m 2 39dm 2 - in square meters; 18 kg 327 g - in kilograms; 937895 mm 3 - in cubic meters, we get:
Cm; m 2; kg; m 3.
Fractions with a denominator of 10, 100, 1000, etc. written without denominator: =0.9; =15.39; =18.327; =0.937895.
0.9; 15.39; 18.327; 0.937895 are decimals.
They have an integer part - the number before the decimal point, and a fractional part - it is written after the decimal point. The fractional part is separated from the integer part by a comma.
Mixed numbers and decimal fractions equal to them are read the same way.
For example, 7 and 7.3 read: seven point three.
The reading of an ordinary and equal decimal fraction is different.
For example,
Reading: seven tenths,
0.7 read: zero point seven.
This means that when writing decimal fractions that do not have an integer part, they write 0 before the fractional part and read “zero integers”.
In the examples below of writing decimal fractions, it turned out that there are as many digits in the numerator of an ordinary fraction as there are zeros in the denominator. The number of digits in the numeral and the number of zeros in the denominator can be different.
For example, let's write it as a decimal fraction. In this mixed number, the numerator of the fractional part has two digits, and the denominator has three zeros. Therefore, first we equalize the number of digits in the numerator and the number of zeros in the denominator: we add one zero before the numerator. We get:
Then = = 23.071
Means,
in order to write a mixed number or an ordinary fraction, in which the denominator is a multiple of 10, as a decimal fraction, you must:
Equalize, if necessary, the number of digits in the numerator and the number of zeros in the denominator by adding zeros in front of the numerator;
Write down the integer part (it can be zero);
Put a comma separating the integer part from the fractional;
Write down the numerator of the fractional part.
For example, = =0.007;14 = =14.000423
The decimal fraction, like a natural number, is divided into digits. The names of the digits of the integer part of a decimal fraction are the same as those of a natural number, and the fractional part is different. The first place to the right of the decimal point is called tenths, next digit - hundredths, and then - thousandths, hundred thousandths etc.
4. The decision to consolidate the new material.
№697
Read the decimals:
1)25,4
2)0,136
3)103,15
4)8,234
5)1,39
6)267,267
7)1015,1
8)307,3078
№698
Read the decimals:
1)36,04
2)0,003
3)181,105
4)0,0809
5)200,7001
6)6,00081
№700
Write decimals:
1) three point sixteen hundredths
2) eight point three hundredths
3) zero point three hundredths
4) twenty eight point seven hundred thousandths
5) four hundred and fifteen millionths
5. The result of the lesson is to announce grades for the lesson, write down d / z.
6. Homework: learn the rule and do the following numbers:
№701 (9-16), №702
Lesson in the 5th grade, teacher-Shabarshova Ekaterina Anatolyevna.
Lesson topic: Decimal fractions. Reading and writing decimals.
Lesson objectives:
Create conditions for the study and repetition of this topic by students;
Development of memory, logic, mathematical thinking;
Raising interest in the subject.
The purpose of the lesson:
Repeat writing and reading decimal fractions;
converting a decimal to a common fraction and vice versa, a common fraction to a decimal.
Lesson type: combined;
Teaching method : verbal, practical, visual.
Form of organization : collective, individual;
Activity content : historical background, survey using signal cards (orally), solving tasks according to the textbook, oral counting "Find a Pair", independent work.
Equipment : signal cards, reflection stickers, self-assessment cards, cards with tasks for independent work.
Lesson Plan :
Organizing time. Emotional mood.
Knowledge update. History reference.
Oral counting "Find a pair."
Textbook work
Independent work.
Student assessment.
Reflection.
Homework.
During the classes:
Organizing time.
Hello guys! Let's greet each other! Turn around to face each other and smile.
Well done! And it is on this pleasant note that we begin our today's lesson!
Intentional division into groups in accordance with the individual characteristics of students.
Write the date in your notebook, cool work. I want to draw your attention to the handouts on your desks, we’ll put the stickers aside for now, and the assessment sheets will come in handy from the first task, as soon as we complete the next task, you must do self-assessment in the sheets when completing this task.
Knowledge update.
Guys, in the last lessons, we began to study the topic “Decimal fraction. Reading and writing decimals. But you and I began to study the topic without knowing its history, a student of our class, Anatoly Shabarshov, who prepared a historical background for us, will help us with this.
History reference.
For the first time, the concept of an abstract decimal fraction arose in the 15th century. It was introduced by the prominent mathematician and astronomer al-Koshi (fullname Jamiad ibn - Masud al - Koshi ) in work"Key to arithmetic" (1427) . The discovery of al-Koshi in Europe became known only after 300 years.
Knowing nothing about the discovery of al-Koshi, decimal fractions were discovered a second time, approximately 150 years after him, by a Flemish mathematician and engineerSimon Stevin in labor"Decimal "(1585).
In Russia, the doctrine of decimal fractions was first issued byL.P. Magnitsky in his "Arithmetic" - the first Russian textbook on mathematics.(1703)
It was proposed to separate the integer part from the fractional part in different ways. Al-Koshi wrote the integer and fractional parts in one row, although he wrote down with different inks, or put a vertical line between them. S. Stevin put a zero in a circle to separate the integer part from the fractional one. The comma accepted in our time was proposed by a German astronomerJ. Kepler (1571 - 1630).
And now let's remember some rules and properties of decimal fractions.
The rules are very simple, if you agree with the statement, then raise a red signal card, if not, then blue. Let's start!
The fractional bar is used to write decimal fractions; (none)
A comma is used to write decimals; (yes)
The integer part of the fraction is before the decimal point; (yes)
If zeros are dropped at the end of the decimal fraction, then the value of the fraction will change; (no)
The digits after the decimal point are called decimal places. (Yes).
2. Well done! Now open your textbooks on page 197, No. 942. (work at the blackboard)
Mental counting "Find a pair"
0,1
0,5
0,2
0,75
0,04
0,05
Textbook work.
№936 (1) - task of the first level of complexity
№951 (1,2) - task of the second level of complexity
№956(1-3) - task of the third level of difficulty
Tasks are calculated individual characteristics of all group members
Independent work.
Option 1
Write as a decimal
; ; ;
Option 2
Write the quotient as a fraction and convert to decimal
5: 100; 5749:100; 34:1000; 324:10.
Option 3
Convert mixed numbers to the denominator 100 and write down the corresponding decimals
Assignments in independent work are compiled taking into account the individual characteristics of students. Options correspond to difficulty levels.
Student assessment.
Students make their own grades for the lesson in the assessment sheets and hand over to the teacher.
Reflection.
Well done guys, everyone did a good job today, so let's summarize:
What new did you learn at the lesson today?
What knowledge and skills did you consolidate today in the lesson?
Did you like the lesson?
Stickers on the table, students write down their attitude to the lesson and stick it on the prepared bulletin board.
Homework
№950,№945
APPS
Task number
Excellent
Good
could do better
Overall grade for the lesson:
Evaluation sheet of the teacher(s): __________________________________________________________
Task number
Excellent
Good
could do better
We will devote this material to such an important topic as decimal fractions. First, let's define the basic definitions, give examples and dwell on the rules of decimal notation, as well as what the digits of decimal fractions are. Next, we highlight the main types: finite and infinite, periodic and non-periodic fractions. In the final part, we will show how the points corresponding to fractional numbers are located on the coordinate axis.
What is decimal notation for fractional numbers
The so-called decimal notation for fractional numbers can be used for both natural and fractional numbers. It looks like a set of two or more numbers with a comma between them.
The decimal point is used to separate the integer part from the fractional part. As a rule, the last digit of a decimal is never a zero, unless the decimal point is immediately after the first zero.
What are some examples of fractional numbers in decimal notation? It can be 34 , 21 , 0 , 35035044 , 0 , 0001 , 11 231 552 , 9 etc.
In some textbooks, you can find the use of a dot instead of a comma (5. 67, 6789. 1011, etc.). This option is considered equivalent, but it is more typical for English-language sources.
Definition of decimals
Based on the above concept of decimal notation, we can formulate the following definition of decimal fractions:
Definition 1
Decimals are fractional numbers in decimal notation.
Why do we need to write fractions in this form? It gives us some advantages over ordinary ones, for example, a more compact notation, especially in cases where the denominator is 1000, 100, 10, etc. or a mixed number. For example, instead of 6 10 we can specify 0 , 6 , instead of 25 10000 - 0 , 0023 , instead of 512 3 100 - 512 , 03 .
How to correctly represent ordinary fractions with tens, hundreds, thousands in the denominator in decimal form will be described in a separate material.
How to read decimals correctly
There are some rules for reading records of decimals. So, those decimal fractions that correspond to their correct ordinary equivalents are read almost the same, but with the addition of the words "zero tenths" at the beginning. So, the entry 0 , 14 , which corresponds to 14 100 , is read as "zero point fourteen hundredths."
If a decimal fraction can be associated with a mixed number, then it is read in the same way as this number. So, if we have a fraction 56, 002, which corresponds to 56 2 1000, we read such an entry as "fifty-six point two thousandths."
The value of a digit in a decimal notation depends on where it is located (just like in the case of natural numbers). So, in decimal fraction 0, 7, seven is tenths, in 0, 0007 it is ten thousandths, and in fraction 70,000, 345 it means seven tens of thousands of whole units. Thus, in decimal fractions, there is also the concept of a number digit.
The names of the digits located before the comma are similar to those that exist in natural numbers. The names of those that are located after are clearly presented in the table:
Let's take an example.
Example 1
We have decimal 43, 098. She has a four in the tens place, a three in the units place, zero in the tenth place, 9 in the hundredth place, and 8 in the thousandth place.
It is customary to distinguish the digits of decimal fractions by seniority. If we move through the numbers from left to right, then we will go from high to low digits. It turns out that hundreds are older than tens, and millionths are younger than hundredths. If we take that final decimal fraction, which we cited as an example above, then in it the senior, or highest, will be the digit of hundreds, and the lowest, or lowest, will be the digit of 10 thousandths.
Any decimal fraction can be decomposed into separate digits, that is, represented as a sum. This operation is performed in the same way as for natural numbers.
Example 2
Let's try to expand the fraction 56, 0455 into digits.
We will be able to:
56 , 0455 = 50 + 6 + 0 , 4 + 0 , 005 + 0 , 0005
If we remember the properties of addition, we can represent this fraction in other forms, for example, as the sum 56 + 0, 0455, or 56, 0055 + 0, 4, etc.
What are trailing decimals
All the fractions we talked about above are trailing decimals. This means that the number of digits after the decimal point is finite. Let's get the definition:
Definition 1
Trailing decimals are a type of decimal that has a finite number of digits after the comma.
Examples of such fractions can be 0, 367, 3, 7, 55, 102567958, 231032, 49, etc.
Any of these fractions can be converted either into a mixed number (if the value of their fractional part is different from zero), or into an ordinary fraction (if the integer part is zero). We have devoted a separate material to how this is done. Let's just point out a couple of examples here: for example, we can bring the final decimal fraction 5 , 63 to the form 5 63 100 , and 0 , 2 corresponds to 2 10 (or any other fraction equal to it, for example, 4 20 or 1 5 .)
But the reverse process, i.e. writing an ordinary fraction in decimal form may not always be performed. So, 5 13 cannot be replaced by an equal fraction with a denominator of 100, 10, etc., which means that the final decimal fraction will not work out of it.
The main types of infinite decimal fractions: periodic and non-periodic fractions
We pointed out above that finite fractions are called so because they have a finite number of digits after the decimal point. However, it may well be infinite, in which case the fractions themselves will also be called infinite.
Definition 2
Infinite decimals are those that have an infinite number of digits after the decimal point.
Obviously, such numbers simply cannot be written completely, so we indicate only a part of them and then put ellipsis. This sign indicates an infinite continuation of the sequence of decimal places. Examples of infinite decimals would be 0 , 143346732 ... , 3 , 1415989032 ... , 153 , 0245005 ... , 2 , 66666666666 ... , 69 , 748768152 ... . etc.
In the "tail" of such a fraction, there can be not only seemingly random sequences of numbers, but a constant repetition of the same character or group of characters. Fractions with alternation after the decimal point are called periodic.
Definition 3
Periodic decimal fractions are such infinite decimal fractions in which one digit or a group of several digits is repeated after the decimal point. The repeating part is called the period of the fraction.
For example, for the fraction 3, 444444 ... . the period will be the number 4, and for 76, 134134134134 ... - the group 134.
What is the minimum number of characters allowed in a periodic fraction? For periodic fractions, it will be sufficient to write the entire period once in parentheses. So, the fraction is 3, 444444 ... . it will be correct to write as 3, (4) , and 76, 134134134134 ... - as 76, (134) .
In general, entries with multiple periods in brackets will have exactly the same meaning: for example, the periodic fraction 0.677777 is the same as 0.6 (7) and 0.6 (77), etc. Entries like 0 , 67777 (7) , 0 , 67 (7777) and others are also allowed.
In order to avoid errors, we introduce the uniformity of notation. Let's agree to write only one period (the shortest possible sequence of digits), which is closest to the decimal point, and enclose it in parentheses.
That is, for the above fraction, we will consider the entry 0, 6 (7) as the main one, and, for example, in the case of the fraction 8, 9134343434, we will write 8, 91 (34) .
If the denominator of an ordinary fraction contains prime factors that are not equal to 5 and 2, then when converted to decimal notation, infinite fractions will be obtained from them.
In principle, we can write any finite fraction as a periodic one. To do this, we just need to add an infinite number of zeros to the right. How does it look on the record? Let's say we have a final fraction 45, 32. In periodic form, it will look like 45 , 32 (0) . This action is possible because adding zeros to the right of any decimal fraction gives us a fraction equal to it as a result.
Separately, one should dwell on periodic fractions with a period of 9, for example, 4, 89 (9), 31, 6 (9) . They are an alternative notation for similar fractions with a period of 0, so they are often replaced when writing with fractions with a zero period. At the same time, one is added to the value of the next digit, and (0) is indicated in parentheses. The equality of the resulting numbers is easy to check by presenting them as ordinary fractions.
For example, the fraction 8, 31 (9) can be replaced by the corresponding fraction 8, 32 (0) . Or 4 , (9) = 5 , (0) = 5 .
Infinite decimal periodic fractions are rational numbers. In other words, any periodic fraction can be represented as an ordinary fraction, and vice versa.
There are also fractions in which there is no infinitely repeating sequence after the decimal point. In this case, they are called non-periodic fractions.
Definition 4
Non-periodic decimal fractions include those infinite decimal fractions that do not contain a period after the decimal point, i.e. repeating group of numbers.
Sometimes non-periodic fractions look very similar to periodic ones. For example, 9 , 03003000300003 ... at first glance seems to have a period, but a detailed analysis of the decimal places confirms that this is still a non-periodic fraction. You have to be very careful with numbers like this.
Non-periodic fractions are irrational numbers. They are not converted to ordinary fractions.
Basic operations with decimals
The following operations can be performed with decimal fractions: comparison, subtraction, addition, division and multiplication. Let's analyze each of them separately.
Comparing decimals can be reduced to comparing ordinary fractions that correspond to the original decimals. But infinite non-periodic fractions cannot be reduced to this form, and converting decimal fractions to ordinary ones is often a laborious task. How to quickly perform a comparison action if we need to do it in the course of solving the problem? It is convenient to compare decimal fractions by digits in the same way as we compare natural numbers. We will devote a separate article to this method.
To add one decimal fraction to another, it is convenient to use the column addition method, as for natural numbers. To add periodic decimal fractions, you must first replace them with ordinary ones and count according to the standard scheme. If, according to the conditions of the problem, we need to add infinite non-periodic fractions, then we must first round them up to a certain digit, and then add them. The smaller the digit to which we round, the higher the accuracy of the calculation will be. For subtraction, multiplication and division of infinite fractions, preliminary rounding is also necessary.
Finding the difference of decimal fractions is the opposite of addition. In fact, with the help of subtraction, we can find a number whose sum with the subtracted fraction will give us the reduced one. We will talk about this in more detail in a separate article.
Multiplication of decimal fractions is done in the same way as for natural numbers. The method of calculation by a column is also suitable for this. We again reduce this action with periodic fractions to the multiplication of ordinary fractions according to the rules already studied. Infinite fractions, as we remember, must be rounded before counting.
The process of dividing decimals is the reverse of the multiplication process. When solving problems, we also use column counts.
You can set an exact correspondence between the end decimal and a point on the coordinate axis. Let's figure out how to mark a point on the axis that will exactly correspond to the required decimal fraction.
We have already studied how to construct points corresponding to ordinary fractions, and decimal fractions can be reduced to this form. For example, an ordinary fraction 14 10 is the same as 1 , 4 , so the point corresponding to it will be removed from the origin in the positive direction by exactly the same distance:
You can do without replacing the decimal fraction with an ordinary one, and take the digit expansion method as a basis. So, if we need to mark a point whose coordinate will be equal to 15 , 4008 , then we will first represent this number as a sum 15 + 0 , 4 + , 0008 . To begin with, we set aside 15 whole unit segments in the positive direction from the origin, then 4 tenths of one segment, and then 8 ten-thousandths of one segment. As a result, we will get a coordinate point, which corresponds to the fraction 15, 4008.
For an infinite decimal fraction, it is better to use this particular method, since it allows you to approach the desired point as close as you like. In some cases, it is possible to build an exact correspondence of an infinite fraction on the coordinate axis: for example, 2 = 1, 41421. . . , and this fraction can be associated with a point on the coordinate ray, remote from 0 by the length of the diagonal of the square, the side of which will be equal to one unit segment.
If we find not a point on the axis, but a decimal fraction corresponding to it, then this action is called the decimal measurement of the segment. Let's see how to do it right.
Suppose we need to get from zero to a given point on the coordinate axis (or get as close as possible in the case of an infinite fraction). To do this, we gradually set aside unit segments from the origin of coordinates until we get to the desired point. After whole segments, if necessary, we measure tenths, hundredths and smaller parts so that the correspondence is as accurate as possible. As a result, we got a decimal fraction that corresponds to a given point on the coordinate axis.
Above we gave a picture with a point M. Look at it again: to get to this point, you need to measure one unit segment from zero and four tenths of it, since this point corresponds to the decimal fraction 1, 4.
If we cannot hit a point in the process of decimal measurement, then it means that an infinite decimal fraction corresponds to it.
If you notice a mistake in the text, please highlight it and press Ctrl+Enter
A common fraction (or mixed number) whose denominator is one followed by one or more zeros (i.e. 10, 100, 1000, etc.):
can be written in a simpler form: without a denominator, separating the integer and fractional parts from each other with a comma (in this case, it is believed that the integer part of a proper fraction is 0). First, the integer part is written, then a comma is placed, and after it the fractional part is written.:
Ordinary fractions (or mixed numbers) written in this form are called decimals.
Reading and writing decimals
Decimal fractions are written according to the same rules by which natural numbers are written in the decimal number system. This means that in decimals, as in natural numbers, each digit expresses units that are ten times larger than the neighboring units on the right.
Consider the following entry:
The number 8 means simple units. The number 3 means units that are 10 times smaller than simple units, i.e. tenths. 4 means hundredths, 2 means thousandths, etc.
The numbers to the right after the decimal point are called decimal places.
Decimal fractions are read as follows: first the whole part is called, then the fractional part. When reading the integer part, it must always answer the question: how many integer units are there in the integer part? . The word whole (or whole) is added to the answer, depending on the number of whole units. For example, one integer, two integers, three integers, etc. When reading the fractional part, the number of shares is called and at the end they add the name of those shares with which the fractional part ends:
3:1 reads: three point one tenth.
2.017 reads like this: two point seventeen thousandths.
To better understand the rules for writing and reading decimal fractions, consider the table of digits and the examples of writing numbers given in it:
Please note that after a decimal point in a decimal fraction, there are as many digits as there are zeros in the denominator of the corresponding ordinary fraction:
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