Nina Shilova
The project of students in grade 6 "Decimal fractions around us"

Project« Decimals around us» Prepared: Parshina Maria, Kopylova Anastasia.

Project motivates independent activity students, initiates their creativity, allows them to express themselves. students choose the necessary piece of information in its large flow, plan and conduct mathematical research, resolving the difficulties along the way. Processing, analysis of the results, their comprehension and presentation are carried out.

Targets and goals project:

Show importance decimal fractions in human life;

Attract attention students to use fractions in various fields of science;

Learn to apply knowledge on the topic « Decimals» on practice;

Develop teamwork and information technology skills.

Object of study - decimals, their properties, history and possibility of application in various fields of science and human life.

1) From the history of occurrence decimal fractions.

2) Decimals around us.

3) Tasks, crosswords, puzzles using decimal fractions

1) From the history of occurrence decimal fractions.

Decimal the system of measures was already used in ancient China, denoting fractional parts of a number in words. Moreover, each subsequent word denoted a smaller or smaller one.

A more generalized view of decimal fractions was introduced by the Central Asian scientist Jamshid Giyaseddin al-Kashi. In 1427 he published The Key of Arithmetic. In this book he writes for the first time decimals in one line, the truth separates fractional and the whole part from each other is not a comma, but writes them in different colors.

Flemish scientist Simon Stevin (1548-1620) published a short work entitled " Tenth", where he explained the recording and the rules for working with decimals. I consider him the inventor decimal fractions.

The comma as a separator first appeared in the work of the Scottish mathematician John Napier (1617), where he proposed to separate the whole part from fractional or dot, or a comma

2) Decimals around us. 1. At school. Mathematics subject .. Petrov Petya, his grades in the journal - 545544 (5+4+5+5+4+4) :6=4,5 So you can put 5.

2. In medicine. Medicine: anaferon. Composition - antibodies to human gamma interferon - 0.003 g; lactose monohydrate - 0.267 g, microcrystalline cellulose - 0.03 g, magnesium stearate - 0.0003 g.

3. At the bank. A certain amount was deposited in the bank at 20% per annum. How many times will the invested amount increase in 5 years if simple interest is charged?

4. In the firm. Company employee said: "The production of our company's products will increase by 200%, or 2 times". Correct her mistake.

3) Tasks, crosswords using decimal fractions.

1. Petya left the house in 8 :00 and went to school. He walked 800 meters at a speed of 5, reached his apartment, took a textbook, ran to school at a speed of 7 km/h. Will Petya have time to get to school and get ready for the lesson, if the school is 1200 meters away, and the lesson starts at 8 :35, and Petya spends 3.5 km/h preparing for the lesson and remembered that he forgot his textbook at home and went back at a speed of 5.5 km/h, minute?

2. 3. Vasya found sunken treasures in the river and brought them home. He decided to sell them to a rich man. But the rich man deceived him for 1,234,567 rubles. How much are treasures really worth if 0.5 grams of treasure costs $120.5 and their weight is 564.67 grams?

3. 1. 2.4 times more beets were harvested from the first plot than from the second one. But from the second one they collected 25.2 tons more beets than from the first one. How many tons of beets were harvested from the first field, and how many from the second field?

4. 1. The first of the three factors is 1.5 and is 32% of the second factor, and the third is 3.9 more than the first. Find the product of these factors!

5. Solve expressions.

1) (28,2-3,8) : 4+8,9= ?

2) 3*2,7+3,11 - 9,22=?

3) (4 :2+8,1-3,15):5=?

6. Task.

Let's say that you decide to jump into the water from a height of 8.8 m and, after flying 5.6 m, change your mind. How many meters will you have to fly involuntarily?

7. 40 grandmothers entered the bus. 0.2 part of the grandmothers bought tickets, and the rest shouted that they had travel card. In fact, only 7 grandmothers had it. How many grandmothers hare?

8. Children run away from the janitor, run from the janitor around the house. The length of the house is 54.3 m, the width is 19.7 m less. The children ran around the house 20 times. How many meters did they run?

10. A square and a rectangle have the same perimeter. The side of the square is 4.9 m, which is 0.7 of the length of the rectangle

1) Find the width of the rectangle

2) How much is the area of the rectangle less than the area of the square?

11. Vovochka crept up to dad and grandfather and shouted: HOORAY! Dad jumped 1.2 m, and grandfather, who survived and not like that, jumped 0.5 m. How many meters did dad jump higher than grandfather?

12. Among the results in slalom and luge shown by athletes at the 1986 Olympic Games in Brazil, determine the best and find how many fractions of a second separate it from the fourth result:

Slalom: Sledge sport:

Men Women Men Women

5) 3 :02,56 4) 2 :04,76 5) 4 :21,576 1) 3 :15,879

3) 2 :03,15 2) 2 :02,31 1) 3 :23,b87 5) 4 :32,675

4) 2 :05,67 1) 1 :02,65 3) 3 :43,456 3)3 :24,876

2) 2 :02,32 1 :03,54 (removed) 2) 3 :32,675 2) 3 :16,876

1) 1 :02,65 3) 2 :,03,54 4) 3 :45,768 4)4 :25,768

13. On an empty honey barrel preserved signature: gross - 256.18 kg, net - 207.7 kg. 194.75 kg of honey was put into it. What should be written on the barrel now?

14. Boots cost 300,000 rubles. The price for them consistently decreased 2 times by 10%. What was the price of boots after the second decrease? 15. Magic square.

Answer:

16. Petya and Vasya saved up for magazines "Young erudite". They wanted to buy 7 magazines, but they lacked 14.7 rubles, and if they bought 5 magazines, they would have 6.5 rubles left. How much money did they have?

17. Piglet blew up a blue balloon in 10.3 minutes, and a green one in 15.7 minutes. How long would it take him to inflate both balloons if he inflated both at the same time?

18. The speed of the Earth around the sun 29.8 km / s, and the speed of Mars is 5.7 km / s less. How many more kilometers will Earth travel than Mars around the sun in 3 seconds, in 4.5 seconds, in 16.8 seconds, in 1 minute?

Tasks for everyone.

Find a pattern and continue row:

a) 33.76; 16.88; 8.44. . .

b) 0.06; 0.18; 0.54. ..

Of the seven matches, the number 1/7 is laid out. How to turn this fraction to number 1/3 without adding or subtracting matches?

Replace the asterisks with the missing ones. numbers:

6*3*785 + 3*4*82 = *9367**

The buyer had 72 rubles. He bought a cap and tie. He spent 0.1 of all money on a cap, and 0.01 of all money on a tie. How much money does the buyer have?

The train travels the distance from Moscow to Leningrad at a speed of 81.3 km/h and spends 8 hours on this distance. What is the distance from Moscow to Leningrad?

From silver, you can make the thinnest wire 1.8 km, which weighs 1g. From 1 year platinum, you can make a wire 60 km long. Can each of you hold in your hand a coil of silver or platinum wire so long that it could be stretched to the moon?

The mass of precious stones is measured in carats, and 1 carat is equal to 0.2 g. The geologist found 2 diamonds. The first - weighing 51 carats, and the second - weighing 10.1 g. Which diamond is more valuable?

Crossword

1. Signed action «+» .

2. Single ....

3. Action when they find out which value is greater.

4. A figure similar to a parallelepiped.

5. Figure without corners.

6. It doesn't matter.

7. Sign «<» .

8. Signed Action «-» .

9. Decimals….

10. This is the name of a lesson in elementary school.

Answer the questions:

1. What fractions were the forerunners decimal?

2. Who proposed the modern notation, that is, the separation of the whole part of the comma?

3. What do they write instead of a comma in countries where they speak English?

4. What part is after the whole?

5. Who is considered the inventor decimal fractions?

Decimals are used in almost all spheres of human activity; do without no decimal fractions; decimals must be studied; knowledge decimal fractions helps people in life.

"Magic Decimals" in 5th grade Educational project

Justification of the significance of the project With decimal fractions, students of the fifth grade meet for the first time. They must learn to operate with fractions as well as with natural numbers, understand the significance of these numbers.

Objectives: Educational: Continuation of work on the formation of a sustainable interest in mathematics and in extracurricular forms of its in-depth study. Learning decimals. Educational: Creation of conditions for relations of cooperation between students, as well as for individual work; formation of a sense of responsibility for the assigned work; listening and listening skills. Developing: Development of students' creative abilities (imagination, observation, memory, thinking); Development of introspection and reflection; Development of the ability to identify causal relationships.

From the history of decimal fractions Decimal fractions appeared in the works of Arab mathematicians in the Middle Ages and independently in ancient China. But even earlier, in ancient Babylon, fractions of the same type were used, only sexagesimal. Later, the scientist Hartmann Beyer () published the essay Decimal Logistics, where he wrote: ... I drew attention to the fact that technicians and artisans, when they measure any length, very rarely and only in exceptional cases express it in whole numbers of one name; usually they have to either take small measures, or turn to fractions, in the same way astronomers measure quantities not only in degrees, but also in fractions of a degree, that is, minutes, seconds, etc., but it seems to me that their division by 60 parts is not as convenient as dividing by 10, by 100 parts, etc., because in the latter case it is much easier to add, subtract, and generally perform arithmetic operations; It seems to me that decimal parts, if introduced instead of sexagesimal, would be useful not only for astronomy, but also for all kinds of calculations.

Here is how they would write the number 3.1415: S. Stevin J. H. Beyer 0 Ι ΙΙ ΙΙΙ ΙV A. Girard 3|1415

Verse about decimal fractions We are not simple fractions, We are not empty signs. We are decimal fractions, Perhaps the usual ones. If we are correct. To the left of us are zeros. Right before the comma - This sign is not easy. The comma is important in us, And it is always needed. Here's an example for you: if your best friend suddenly wrote about the unit, that it is equal to one tenth. But it's so terrible And he tried in vain! Children, always remember: The comma is important in us!

And here is another rule, it is not more difficult: If at the end of decimal fractions Zeros are discarded or attributed, Yes, at least write the whole notebook with zeros! A fraction equal to this will turn out, So why then suffer? To compare decimal fractions, you do not need to learn a lot. Equalize the number of decimal places, assign zeros to one of them on the right. And, discarding the comma later, Compare the right with the left with a number. To subtract or add us, you should not hurry.

Here we can give advice: Write us under each other. A comma so that it is under a comma, And it is necessary to add it up as if there were none of them. And then pay attention, What is possible without much effort to you at the very end, in her answer, Just put in your place. Now that you know everything about us, And now you understand a lot. Remember, we are decimal fractions, And you are probably familiar. And yet, when you come to a decision, think it over carefully.

Fairy tale about decimal fractions In the city where fractions lived, such as (12/10), (289/100), (1872/10000), (5/100) and in general with denominators 10, 100, 1000, etc. ., all lived very friendly. No one beat anyone, did not offend, and no one argued. There were beautiful houses in this city, and there were beautiful flowers on the windows. Each fraction had its own house and garden. Bulk apples, cherries, pears, and various other flowers grew in the garden. There were also schools there. Small fractions went there, with a denominator of 10. There were also adult fractions, with denominators from 100 to, and very old ones, with a denominator from and to infinity. Adult fractions ran to work.

Well, the old men and old women sat all day in rocking chairs and read books, and sometimes they spanked fractions on the asses - babies for disobedience or pranks, or read fairy tales to them. But one day Shtrih attacked the city with his army. He mercilessly killed everyone, burned houses, robbed them. The war lasted for ten years. First one won, then the other, but no one could win the war. But one kind Wizard helped the helpless fractions. He extinguished the burning houses, returned the loot and drove the Stroke away. Only one question worried the Magician: How to cure the wounded shots? He thought for a long time and finally came up with an idea. Instead of a fractional line, he gave fractions commas, removed the denominators, and added 1, 2, 3, etc. zeros after the integer part to the right, depending on how many there were in denominator.

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Presentation on the topic: Magic Decimals

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On a typical day after school, my two best friends, fifth-grade students Anna and Tanya, were doing their math homework. They opened the textbook and saw decimal fractions... On an ordinary day after school, two best friends, fifth-grade students Anna and Tanya were doing their homework in mathematics. They opened the textbook and saw decimal fractions... I don't understand anything! What's happened? These ... like them ... but ... decimal fractions. We didn't pass them! Tanya was outraged. Solve the problem with decimal fractions - Anna reads. - In the spring, they sowed 0.9 fields, and harvested only 0.6 fields. How much crop was not harvested from the field?

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All the same, they sowed 0 or 9? Tanya asked. All the same, they sowed 0 or 9? Tanya asked. Maybe add 9 to 0? Anna suggested. No, we should probably choose 0 or 9 ourselves! Anna agreed. And just as the girls wanted to write it down, the textbooks began to dance and sing: We really need decimal fractions. What is a crooked letter? Or is it a comma? But what does the comma have to do with it, Maya the fairy will tell us!

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Decimal fractions appeared in the works of Arab mathematicians in the Middle Ages and independently in ancient China. But even earlier, in ancient Babylon, fractions of the same type were used, but of course sexagesimal. Decimal fractions appeared in the works of Arab mathematicians in the Middle Ages and independently in ancient China. But even earlier, in ancient Babylon, fractions of the same type were used, but of course sexagesimal. Later, the scientist Hartmann Beyer (1563-1625) published the essay “Decimal Logistics” where he wrote: “... I noticed that technicians and artisans, when they measure any length, very rarely and only in exceptional cases express it in whole numbers of the same name; usually they have to either take small measures, or turn to fractions, in the same way astronomers measure quantities not only in degrees, but also in fractions of a degree, i.e. minutes, seconds, etc., but it seems to me that dividing them into 60 parts is not as convenient as dividing by 10, into 100 parts, etc., because in the latter case it is much easier to add, subtract and generally perform arithmetic operations ; It seems to me that decimal parts, if introduced instead of sexagesimal, would be useful not only for astronomy, but also for all kinds of calculations. Simon Stevin introduced decimal fractions into European practice. Until then, anyone who dealt with non-integer numbers had to fiddle with numerators and denominators.

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Today we use decimals naturally and freely. However, what seems natural to us served as a real stumbling block for the scientists of the Middle Ages. Western Europe in the 16th century along with the widespread decimal system for representing integers, sexagesimal fractions were used everywhere in calculations, dating back to the ancient tradition of the Babylonians. It took the bright mind of the Dutch mathematician Simon Stevin to bring the record of both integer and fractional numbers into a single system. Apparently, the impetus for the creation of decimal fractions was the tables of compound interest compiled by him. In 1585 he published the book Tithing, in which he explained decimal fractions. Stevin's notation was not perfect, just like the notation of his colleagues and followers. This is how they would write the number 3.1415: Today we use decimals naturally and freely. However, what seems natural to us served as a real stumbling block for the scientists of the Middle Ages. Western Europe in the 16th century along with the widespread decimal system for representing integers, sexagesimal fractions were used everywhere in calculations, dating back to the ancient tradition of the Babylonians. It took the bright mind of the Dutch mathematician Simon Stevin to bring the record of both integer and fractional numbers into a single system. Apparently, the impetus for the creation of decimal fractions was the tables of compound interest compiled by him. In 1585 he published the book Tithing, in which he explained decimal fractions. Stevin's notation was not perfect, just like the notation of his colleagues and followers. This is how they would write the number 3.1415:

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We have heard a lot about air. Air is 99.96% composed of three gases: nitrogen, oxygen and argon. Carbon dioxide contains 0.03%, the rest accounts for 0.01%. We have heard a lot about air. Air is 99.96% composed of three gases: nitrogen, oxygen and argon. Carbon dioxide contains 0.03%, the rest accounts for 0.01%.

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Of great importance for the knowledge of the world is the problem of the numerical ratio between the atoms of various elements. Of great importance for the knowledge of the world is the problem of the numerical ratio between the atoms of various elements. If we compare the iron, cobalt and nickel available on the whole Earth, it turns out that the globe consists of: Iron 92% Cobalt 0.5% Nickel 7.5% The most accurate chemical analyzes of a huge number of meteorites that fell to Earth gave wonderful results. It turned out that in iron meteorites the percentage of iron, cobalt and nickel amazingly coincides with their content on our planet.

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You can tell me a lot, You can tell me a lot, About what decimal fractions are, About what you can at the end of the fractional part, To the right, discard or insert zeros. Well, how to compare them, you tell me. Well, it's certainly easier than ever. Compare the whole parts of the decimal fraction, And the one that has more of it, Of course, there will be more. Well, if those parts are just equal, Then what should I do, you tell me. If two decimal fractions have equal integer parts, You look at the first of the mismatched digits, And the one with the larger one, of course, will also have the larger one. Do you remember everything, you tell me?

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Vasya found sunken treasures in the river and brought them home. He decided to sell them to a rich man. But the rich man deceived him for 1,234,567 rubles. How much are treasures really worth if 0.5 grams of treasure costs $120.5 and their weight is 564.67 grams? Vasya found sunken treasures in the river and brought them home. He decided to sell them to a rich man. But the rich man deceived him for 1,234,567 rubles. How much are treasures really worth if 0.5 grams of treasure costs $120.5 and their weight is 564.67 grams?

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The cabbage butterfly caterpillar eats 10g per month. cabbage. The tit eats 100 caterpillars daily. Calculate how much cabbage "saves" for 1 month (30 days) a family of tits consisting of a female, a male and 4 chicks, if we assume that the chick eats 2 times less than an adult tit. The cabbage butterfly caterpillar eats 10g per month. cabbage. The tit eats 100 caterpillars daily. Calculate how much cabbage "saves" for 1 month (30 days) a family of tits consisting of a female, a male and 4 chicks, if we assume that the chick eats 2 times less than an adult tit.

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Kolya dreamed of a chocolate bar that was 3.7 meters long and 2.1 meters wide. Tolya dreamed of a chocolate bar of the same length, but three times as large as Kolya's. By how many meters is the width of the chocolate that Tolya dreamed of longer than the width that Kolya dreamed of? Kolya dreamed of a chocolate bar that was 3.7 meters long and 2.1 meters wide. Tolya dreamed of a chocolate bar of the same length, but three times as large as Kolya's. By how many meters is the width of the chocolate that Tolya dreamed of longer than the width that Kolya dreamed of?

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The inscription remained on the empty container: GROSS - 21.8 kg, NET - 20.6 kg. 19.9 kg of oil was put into it. What should be written on the container now? The inscription remained on the empty container: GROSS - 21.8 kg, NET - 20.6 kg. 19.9 kg of oil was put into it. What should be written on the container now?

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Duck Donna Duck decided to make an apple pie. For this, she took: 0.57 kg of apples, 2 cups of flour, 0.25 kg each, 0.01 kg of butter, 2 cups of milk and 2 eggs. How much will the cake weigh when Donna Duck takes it out of the oven? How much will the pie weigh when Donna Duck's nephews eat 1/3 of the pie? Duck Donna Duck decided to make an apple pie. For this, she took: 0.57 kg of apples, 2 cups of flour, 0.25 kg each, 0.01 kg of butter, 2 cups of milk and 2 eggs. How much will the cake weigh when Donna Duck takes it out of the oven? How much will the pie weigh when Donna Duck's nephews eat 1/3 of the pie?

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In the city where fractions lived, such as 1 2/10, 2 98/100, 1872/10000, 5/100 and in general with denominators 10, 100, 1000, etc., everyone lived very friendly. No one beat anyone, did not offend, and no one argued. There were beautiful houses in this city, and there were beautiful flowers on the windows. Each fraction had its own house and garden. Bulk apples, cherries, pears, and various other flowers grew in the garden. In the city where fractions lived, such as 1 2/10, 2 98/100, 1872/10000, 5/100 and in general with denominators 10, 100, 1000, etc., everyone lived very friendly. No one beat anyone, did not offend, and no one argued. There were beautiful houses in this city, and there were beautiful flowers on the windows. Each fraction had its own house and garden. Bulk apples, cherries, pears, and various other flowers grew in the garden. There were also schools there. Small fractions went there with a denominator of 10. There were also adult fractions with denominators from 100 to 100,000 and very old ones with a denominator from 100,000 to infinity. Adult fractions ran to work.

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Well, the old men and women sat in rocking chairs all day and read books, and sometimes they spanked the bottoms of baby shots for disobedience or pranks, or read fairy tales to them. Well, the old men and old women sat all day in rocking chairs and read books. , and sometimes slapped on the bottoms of baby shots for disobedience or pranks, or read fairy tales to them. But one day Shtrikh attacked the city with his army. He mercilessly killed everyone, burned houses, robbed them. The war lasted for ten years. First one won, then the other, but no one could win the war. But one kind Wizard helped the helpless fractions. He extinguished the burning houses, returned the loot and drove the stroke away. Only one question worried the Wizard: "How to cure the wounded shots?". He thought for a long time, and finally came up with. Instead of a fractional line, he gave fractions commas, removed denominators, and such fractions as 1/100, 32/1000, etc. added after the integer part on the right 1, 2, 3, etc. zeros, depending on how many there were in the denominator.

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So the girls' journey through the kingdom of decimal fractions ended. On this journey, they learned a lot of new things, and now they can do any problem with decimal fractions! So the girls' journey through the kingdom of decimal fractions ended. On this journey, they learned a lot of new things, and now they can do any problem with decimal fractions!

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INTRODUCTION On the most ordinary day after school, two best friends, 6th grade students Alyosha and Ruslan were doing their homework in mathematics. They opened the textbook and saw decimal fractions... I don't understand anything! What's happened? These ... like them ... but ... decimal fractions. We didn't pass them! Alyosha was outraged. Solve the problem with decimal fractions - Ruslan reads. - In the spring, they sowed 0.9 fields, and harvested only 0.6 fields. How much crop was not harvested from the field?

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All the same, they sowed 0 or 9? Alyosha asked. Maybe add 9 to 0? Ruslan suggested. No, we should probably choose 0 or 9 ourselves! Ruslan agreed. And as soon as the boys wanted to write it down, the textbooks began to dance and sing: We really need decimal fractions. What is a crooked letter? Or is it a comma? But what does the comma have to do with it, Maya the fairy will tell us!

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The Kingdom of Decimals 1st castle where you will learn about the history of decimals 2nd castle where you will learn interesting facts about decimals 3rd castle where you will learn how to perform operations with decimals 4th castle where you will meet with fascinating tasks in which there are decimal fractions 5th castle, where you will be told a fairy tale about decimal fractions Exit the kingdom

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From the history of decimal fractions Decimal fractions appeared in the works of Arab mathematicians in the Middle Ages and independently in ancient China. But even earlier, in ancient Babylon, fractions of the same type were used, but of course sexagesimal. Later, the scientist Hartmann Beyer (1563-1625) published the essay “Decimal Logistics” where he wrote: “... I noticed that technicians and artisans, when they measure any length, very rarely and only in exceptional cases express it in whole numbers of the same name; usually they have to either take small measures, or turn to fractions, in the same way astronomers measure quantities not only in degrees, but also in fractions of a degree, i.e. minutes, seconds, etc., but it seems to me that dividing them into 60 parts is not as convenient as dividing by 10, into 100 parts, etc., because in the latter case it is much easier to add, subtract and generally perform arithmetic operations ; It seems to me that decimal parts, if introduced instead of sexagesimal, would be useful not only for astronomy, but also for all kinds of calculations. Simon Stevin introduced decimal fractions into European practice. Until then, anyone who dealt with non-integer numbers had to fiddle with numerators and denominators.

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From the history of decimal fractions Why did people switch from ordinary fractions to decimals? Yes, because the actions with them are simpler, especially addition and subtraction. Add the fractions 3/50 and 7/40. First you need to find the least common multiple of their denominators (this is the number 200), then divide it by 50 and multiply the result (the number 4) by the numerator and the denominator of the first fraction. It turns out 12/200. Then you need to divide 200 by 40 and multiply the quotient (number 5) by the numerator and denominator of the second fraction. It turns out 35/200. We reduced fractions to a common denominator. Only now can we add up the numerators and get the answer: 47/200. And if these fractions are presented as a decimal notation: 3/50=0.06; 7/40 \u003d 0.175, the amount is instantly - this is 0.235. Of course, the number 1/7 has to be written only with a certain accuracy, 0.143 or 0.14287, but everything in life has its limits of accuracy. Only in the first quarter of the 18th century. fractional numbers began to be written using a simple decimal point. In some countries, and in particular in Russia, a comma is used instead of a dot. It was introduced by the German mathematician Georg Andreas Böckler in 1661.

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From the history of decimals Today we use decimals naturally and freely. However, what seems natural to us served as a real stumbling block for the scientists of the Middle Ages. Western Europe in the 16th century along with the widespread decimal system for representing integers, sexagesimal fractions were used everywhere in calculations, dating back to the ancient tradition of the Babylonians. It took the bright mind of the Dutch mathematician Simon Stevin to bring the record of both integer and fractional numbers into a single system. Apparently, the impetus for the creation of decimal fractions was the tables of compound interest compiled by him. In 1585 he published the book Tithing, in which he explained decimal fractions. Stevin's notation was not perfect, just like the notation of his colleagues and followers. This is how they would write the number 3.1415:

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It's interesting We've heard a lot about air. Air is 99.96% composed of three gases: nitrogen, oxygen and argon. Carbon dioxide contains 0.03%, the rest accounts for 0.01%. Substance Content in air (vol %) dry wet N2 O2 H2O Ar CO2 Other 78.08 20.95 --- 0.93 0.03 0.01 76.28 20.47 2.31 0.98 0.03 0 .01

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This is interesting. The problem of the numerical ratio between the atoms of various elements is of great importance for the knowledge of the world. If we compare the iron, cobalt and nickel available on the whole Earth, it turns out that the globe consists of: Iron 92% Cobalt 0.5% Nickel 7.5% The most accurate chemical analyzes of a huge number of meteorites that fell to Earth gave wonderful results. It turned out that in iron meteorites the percentage of iron, cobalt and nickel amazingly coincides with their content on our planet.

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A verse about decimal fractions You can tell me a lot, About what decimal fractions are, About what you can at the end of the fractional part, To the right, discard or insert zeros. Well, how to compare them, you tell me. Well, it's certainly easier than ever. Compare the whole parts of the decimal fraction, And the one that has more of it, Of course, there will be more. Well, if those parts are just equal, Then what should I do, you tell me. If two decimal fractions have equal integer parts, You look at the first of the mismatched digits, And the one with the larger one, of course, will also have the larger one. To begin with, the number of decimal places, you equalize, Write them in a column and of course, know That the comma should be under the comma, And then just decide. Do the addition or subtraction first, without paying any attention to the comma. Well, in your answer, of course, you put a comma under the comma in these fractions. You remember these rules forever, so that in your memory they remain like twice two!

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Task 1 Vasya found sunken treasures in the river and brought them home. He decided to sell them to a rich man. But the rich man deceived him for 1,234,567 rubles. How much are treasures really worth if 0.5 grams of treasure costs $120.5 and their weight is 564.67 grams?

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Task 2 The cabbage butterfly caterpillar eats 10g per month. cabbage. The tit eats 100 caterpillars daily. Calculate how much cabbage "saves" for 1 month (30 days) a family of tits consisting of a female, a male and 4 chicks, if we assume that the chick eats 2 times less than an adult tit.

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Problem 3 Kolya dreamed of a chocolate bar 3.7 m long and 2.1 m wide. Dima dreamed of a chocolate bar of the same length but three times as large as Kolya's. By how many meters is the width of the chocolate that Tolya dreamed of longer than the width that Kolya dreamed of?

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Problem 4 On the empty container, the inscription was preserved: GROSS - 21.8 kg, NET - 20.6 kg. 19.9 kg of oil was put into it. What should be written on the container now?

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Problem 5 Duck Donna Duck decided to make an apple pie. For this, she took: 0.57 kg of apples, 2 cups of flour, 0.25 kg each, 0.01 kg of butter, 2 cups of milk and 2 eggs. How much will the cake weigh when Donna Duck takes it out of the oven? How much will the pie weigh when Donna Duck's nephews eat 1/3 of the pie?

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Description of the slide:

We will try to place these and many other tasks in the collection of tasks released by the 6th grade!

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