Recording and reading decimal fractions. Decimal fractions
Ordinary fraction (or mixed number), in which the denominator is a unit with one or more zeros (i.e. 10, 100, 1000, etc.):
it can be written in a simpler form: without a denominator, separating the whole and fractional parts from each other of the comma (it is believed that the whole part of the correct fraction is 0). At first, the whole part is recorded, then the comma is put, and after it the fractional part is written.:
Recorded ordinary fractions (or mixed numbers) are called decimal fractions.
Reading and recording decimal fractions
Decimal fractions are recorded according to the same rules on which natural numbers are recorded in a decimal number system. This means that in decimal fractions, as in natural numbers, each figure expresses units that are ten times more neighboring units standing on the right.
Consider the following entry:
Figure 8 means simple units. Figure 3 means units, 10 times smaller than simple units, i.e. tenths. 4 means hundredths of shares, 2 - thousandth, etc.
Numbers that stand on the right after the comma are called decimal signs.
Decimal fractions read as follows: First, the whole part is called, then fractional. When reading the whole part, it should always be responsible for: how many units are contained in the whole part? . The answer is added by the word whole (or a whole), depending on the number of entire units. For example, one whole, two integers, three integers, etc., when reading a fractional part, is called the number of fractions and at the end add the name of those fractions that the fractional part ends:
3.1 reads: three integer one tenth.
2.017 reads: two whole seventeen thousandths.
To better understand the rules for recording and reading decimal fractions, Consider the discharge table and the examples of the recording numbers given in it:
Note, after the semicolons in the decimal record, there are so many digits as zeros containing a denominator of an ordinary fraction corresponding to it:
Lessonmathematics in grade 5 on the topic "Decimal record of fractional numbers"
Subject: The concept of decimal fraction. Reading and recording decimal fractions.
The purpose of the lesson:enter the concept of decimal fractions, the correct reading and record.
Tasks:
To organize the work of students on the study and primary consolidation of the concept of "decimal fraction", an algorithm for recording decimal fractions.
Create conditions for forming a Wood:
Communicative Wood: The ability to listen, discipline, independence of thinking.
Regulatory Wood: Understand the learning task of the lesson, make a decision task under the guidance of the teacher, determine the goal task, control your actions in the process of execution, detect and correct errors, respond to final questions and evaluate your achievements.
Personal Wood: Formation of learning motivation, the need to acquire new knowledge.
Type of lesson: Lesson studying new material
Lesson building technology: problem method, work in pairs
Work forms: individual, frontal, conversation, work in pairs.
Organization of students in the lesson:
Independently go to the problem and solve it;
Independently determine the topic, objectives of the lesson;
Derive a rule;
Work with textbook text;
Answer questions;
Solve their own tasks;
Evaluate yourself and each other;
Reflect.
Teaching methods: verbally, clearly illustrative, practical
Resources:multimedia projector, presentation.
Educational and Methodical Provision: Tutorial"Mathematics. Grade 5 »Author N.Ya. Vilenkin; CD "Mathematics. Teaching on new standards. Theory. Technique. Practice. Publishing House "Teacher".
| Stage lesson | Teacher's activities | Activity student |
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| 1. Org. moment Determination of needs and motifs. 1 min | Hello guys! I would like to start a lesson from the words of the famous German poet and thinker I. Goethe: « The numbers (numbers) do not control the world, but they show how the world is managed. " And today with you also plunge into the world of numbers and numbers. | Greeting students; Checking the readiness of the class to the lesson; Organization of attention. | Greet teachers |
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| 2. Setting goals and objectives, actualization of knowledge | Guys raise hands, who at least once saw records of the form: 3.5 and 1.56 Guys, where did you meet these records? These records indicate the fractions. The name of these fractions is encrypted. Let's formulate the topic together together. Today we are starting to explore a very important, interesting and new topic for you. And what would you like to know interesting and new about decimal fraction? Today at the lesson we will learn to record fractional numbers in a new way. Write down theme lesson "Decimal record of fractional numbers" (slide ) . Read the fractions. What two groups can they divide them? But not to all ordinary fractions you can apply a new record Who guessed, to what? | Asking questions. Offers answering questions. | Guys guess the rebus. Students formulate the subject of lesson. Determine the objectives of the lesson. Record theme lesson. Read fractions. -All fractions in the denominator unit and zeros. -Right and wrong |
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| 3. Studying a new material | How to record fractional numbers differently? Look at the table ( slide ).
So the problem was how to record ordinary fractions, Mixed numbers - in a new way. | Consider how to burn a mixed number with a decimal fraction: (write to the notebook) From the considered examples we will conclusions, get the rule What pattern did you notice? A. 0.037 A. 3,5216 Make an algorithm for the transfer of ordinary fractions to decimal. | the number of zeros coincides with the number of numbers after the comma Students constitute an algorithm for the transfer of ordinary fractions to decimal. |
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| 4. Fizkultminutka | http://videouroki.net/ | ||||||||||||||||||||||||||||||
| 5. Primary consolidation, pronouncing in external speech | In Russia, for the first time about decimal fractions, it was said in the Russian textbook of mathematics - "arithmetic". We can recognize his author if we write fractions and mixed numbers with decimal fractions. (Mixed numbers are written on the board, and decimal fractions - on cards, on back side Which is the letter. In the course of the task, students make a word.) (M) Exercise on the textbook: 1117, 1120 | The primary consolidation is carried out through the commenting of each such situation, it is pronounced out loud to the actions established by the algorithm (what I do, why what follows what happens | Students get the word " Magnitsky " |
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| 6.Independent work. Check on the standard. | 1. Work in the notebook(independently). Write in the notebook the correct fractions (in the column). Replace their decimal fractions. Check (slide ) Now write wrong fractions and replace them with decimal. Check (slide ) | ||||||||||||||||||||||||||||||
| 7. Evaluation of the lesson results. Summing up the lesson (reflection). | What topic are we studied today? What tasks we put today? Our tasks are completed? | Answer questions. |
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| 8. Information about the homework. | Homework. Find information (articles, some other data in any periodical literature), in which there is a record of decimal fractions. Perform № 1139,1144 (a) Explore paragraph 30 | Students record homework depending on the level of lesson theme |
Subject: decimal fractions. Addition and subtraction of decimal fractions
Lesson: Decimal record of fractional numbers
The denomoter denominator can be expressed by any natural number. Fractional numbers in which the denominator is expressed by a number 10; 100; 1000; ..., where n, it was agreed to record without a denominator. Anyone fractional number, in the denominator of which 10; 100; 1000, etc. (i.e. a unit with several zeros) can be represented as a decimal record (in the form of a decimal fraction). First, they write a whole part, then the numerator of the fractional part, and the whole part of the fraction is separated.
For example,
If the whole part is absent, i.e. The crushing is correct, then the whole part is written in the form of 0.
In order to correctly record a decimal fraction, the slurner of the fractional part should have the same signs as zeros in the fractional part.
1. Record in the form of a decimal fraction.
2. Present a decimal fraction in the form of a fraction or mixed number.
3. Read the decimal fractions.
12.4 - 12 as many as 4 tenths;
0.3 - 0 as many as 3 tenths;
1.14 - 1 whole 14 hundredths;
2.07 - 2 as many as 7 hundredths;
0.06 - 0 as many as 6 hundredths;
0.25 - 0 as many as 25 hundredths;
1.234 - 1 whole 234 thousands;
1,230 - 1 whole 230 thousand thousand;
1,034 - 1 whole 34 thousands;
1.004 - 1 whole 4 thousandths;
1,030 - 1 whole 30 thousands;
0,010101 - 0 as many as 10101 million.
4. Transfer the comma in each digit to 1 discharge left and read the numbers.
34,1; 310,2; 11,01; 10,507; 2,7; 3,41; 31,02; 1,101; 1,0507; 0,27.
5. Transfer the comma in each of the numbers to 1 discharge to the right and read the resulting number.
1,37; 0,1401; 3,017; 1,7; 350,4; 13,7; 1,401; 30,17; 17; 3504.
6. Express meters and centimeters.
3.28 m \u003d 3 m +.
7. Express tons and kilograms.
24,030 T \u003d 24 tons.
8. Write in the form of a decimal fraction private.
1710: 100 = 
;
64: 10000 = 
803: 100 = 
407: 10 = 
9. Express DM.
5 dm 6 cm \u003d 5 dm + 
;
9 mm \u003d. 
Subject: Mathematics Class:5
Theme lesson: "Decimal. Reading and recording decimal fractions. "
Objectives lesson:
training: Examine the concept of decimal fractions, learn to read and write down decimal fractions, form the skill of reading and writing a decimal fraction;developing: develop logical thinking, ability to analyze, compare, summarize, draw conclusions, develop attention;educational: educating in students hard work, accuracy, self-control skills, friendliness, mutual arms.
Type of lesson:studying a new material.
Teaching methods:sensual, practical, individual.
Lesson plan:
1. Organizational moment.
2. Oral survey.
3. Just a new material.
3. Consideration of examples, orally.
4. Fastening knowledge.
5. Estimates for the lesson.
6. Setting the task of the house.
During the classes:
1. Org.Moment.
Hello guys! Sit down! (The magazine is filled, missing students are noted).
2. Oral survey:
a) What are the fractions with you?
b) What are ordinary fractions?
c) What actions on ordinary fractions can we perform?
Today in the lesson we will get acquainted with new fractions - decimal.
3. Studying a new material.
Among ordinary fractions and mixed numbers, fractions are often found with a denominator, a multiple number 10. 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 will get:
Cm; m 2; kg; m 3.
Fractions with denominator 10, 100, 1000, etc. Recorded without a denominator: \u003d 0.9; \u003d 15.39; \u003d 18,327; \u003d 0.937895.
0.9; 15.39; 18,327; 0,937895 is decimal fractions.
They have a whole part - a number that is up to the comma, and the fractional part - it is recorded after the comma. The fractional part is separated from the part of the comma.
Mixed numbers and equal decimal fractions are read equally.
For example, 7 and 7.3 read: seven as many as three tenths.
Reading an ordinary and equal decimal fraction varies.
For example,
Read: Seven Tenths,
0.7 read: zero seven tenths.
Therefore, when recording decimal fractions, which there is no whole part, write 0 before fractional part and read "zero integers."
In the examples of the decimal fraction below, it turned out that in a numerator of an ordinary fraction as many numbers as zeros in the denominator. The number of numbers in numen and the number of zeros in the denominator can be different.
For example, we will write in the form of a decimal fraction. In this mixed number in the sluple of the fractional part, two digits, in the denominator three zero. Therefore, at first equalize the number of numbers in the numerator and the number of zeros in the denominator: before the numerator we will assign one zero. We get:
Then \u003d \u003d 23,071
It means
to make a mixed number or ordinary fraction, which is Katten 10 denominator, write in the form of a decimal fraction, it is necessary:
Equal, if necessary, the number of numbers in the numerator and the number of zeros in the denominator, attributing the zeros before the numerator;
Write a whole part (it can be zero);
Put the comma separating the whole part of the fractional;
Write a piece of fractional part.
For example, \u003d \u003d 0.007; 14 \u003d \u003d 14.000423
The decimal fraction, as a natural number, is divided into discharge. The name of the discharges of the whole part of the decimal fraction is the same as in the natural number, and the fractional part is the others. The first to the right of the semicolon discharge a decimal fraction is called tenth, the next discharge - hundredths, and then - thousands, hundredsmatesetc.
4. Decision on fixing a new material.
№697
Read decimal fractions:
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 decimal fractions:
1)36,04
2)0,003
3)181,105
4)0,0809
5)200,7001
6)6,00081
№700
Write down decimal fractions:
1) three whole sixteen hundredths
2) eight more three hundredths
3) zero for three hundredths
4) Twenty-eight whole seven hundredsmatic
5) four hundred whole fifteen million
5. The result of the lesson declare estimates for the lesson, write down d / s.
6. Homework: learn the rule and execute the following numbers:
№701 (9-16), №702
Subject:
Purpose: introduce students with new numbers - decimal fractions, form knowledge and
Type of lesson:
Equipment:
tasks.
View the contents of the document
"Abstract lesson on the topic" The concept of decimal fraction. Reading and recording decimal fractions. ""
Subject: The concept of decimal fraction. Reading and recording decimal fractions.
Purpose: introduce students with new numbers - decimal fractions, form knowledge and
possession of mathematics methods; Rail a culture of mathematical thinking.
Type of lesson: Lesson studying a new material.
Equipment: computer at the teacher, screen, multimedia projector; On the tables: Sheets with
tasks.
LESSON STRUCTURE:
Organizing time.
Guys, today at the lesson you have to open a new knowledge, but, as you know, every new knowledge is connected with what we have already studied. Therefore, let's start with the repetition.
Preparation for the study of a new material.
Decide anagram: fraction, angle, numerator, denominator.
Read the numbers in the discharge table.
From the proposed numbers, select: Natural numbers, correct fractions, incorrect fractions, mixed numbers.
Familiarization with new material.
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| Our lesson will be dedicated The topic of the lesson "The concept of decimal fraction. Reading and recording decimal fractions. " The motto of the lesson: knowledge of the "fraction of decimal". |
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| Recall how the decimal number system is arranged. Consider the discharge table and answer questions: Questions: Read the numbers recorded in the table. How is the position of the unit in each next line compared to the previous one? How does the magnitude of the corresponding number change? What arithmetic action matches this change? Output : By moving the unit to one category to the right, each time reduced the corresponding number 10 times and did it until they reached the last discharge - the discharge of units. Is it possible to reduce the unit 10 times? Problem: But there is no place for this number in our category of discharges. I don't have it. To change, how to change the discharge table so that you can write a number in it. |
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| We argue, you need to move the number 1 to the right to one category. But on the right of the discharge of units there are no discharges, then you need to add another column. Come up with the name for this column: tenths. Similarly, arguing: (hundredths) and: 10t. \u003d (thousandth), etc. |
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| Since we reasoned correctly, we turn out the following table: |
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| 2 units of 3 tenths. And to burn numbers outside the table, we need to separate anyone familiar from the fractional. Agreed to do it with a comma or point. In our country, as a rule, a comma is used, and in the US and some other countries - a point. Numbers read as follows: a) 2.3 or 2.3 (two integers three tenths or two, comma, three or two, point, three) |
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| We made a discovery. And this discovery is a dealer to read and write decimal fractions. We have coincided with the rule, which was offered by the author of the textbook. Rule: If a comma (or point) is used in the decimal record of the number, they say that the number is recorded as a decimal fraction. For brevity, the numbers are called simply decimal fractions. |
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| In science and industry, in agriculture Decimal fractions are used much more often than ordinary fractions. This is due to the simplicity of the calculation rules with decimal fractions, they look at the rules of action with natural numbers. 1703 - In Russia, the doctrine of decimal fractions outlined Leontius Filippovich Magitsky in the textbook "Arithmetic, siren science numeral". |
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| We have every reason in order to perform tasks on the lesson. First task. Read the number |
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| Read decimal fractions What can be said about these three numbers? (they are equal) What conclusion can be made about zeros that the decimal fraction ends? (You can not write them, they do not change the number) At the end of the decimal fraction, it is possible to attribute zeros or discard zeros, the decimal fraction will not change from this. The same fraction is written. |
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| Between the whole and fractional parts put a comma. In the absence of any discharge of shares, it is replaced with 0 when recording a number. The number of numbers after the comma should be equal to the number of zeros in the valve of the ordinary fraction. Record with a decimal fraction: |
| Write decimal fractions under dictation. 7 as many as 8 tenths 2 whole 25 hundredths 0 whole 92 hundredths 12 whole 3 hundredths 5 whole 187 thousand 24 Whole 24 thousandth 7 As many as 7 tenths 7 whole 7 hundredths 7 whole 7 thousandths 0 whole 5 decades Now we carry out independent work, when performing your knowledge on the subject of the lesson. |
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| Independent work (5 minutes) |
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| Check yourself: Write in the form of a decimal fraction (in a line); Check the answers on the table by putting each number the corresponding letter (under each number without punctuation) What word did it work? WELL DONE |
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| Reflection |
| Homework: №647 a), 648 AB), 649 a), 650 V) |
