Cabinetmaker. In 1921 he became one of the founders of the Communist...
"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.
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 a book of tithes in which he explained decimals. Stevin's notation was not perfect, just like the notation of his colleagues and followers.
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.
A fairy tale about decimal fractions In a 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
slide number 1
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slide number 2
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On the most ordinary day after school, two best friends, fifth grade students Anna and Tanya did homework mathematics. 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? 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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slide number 5
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slide number 6
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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.
slide number 7
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slide number 8
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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%.
slide number 10
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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.
slide number 11
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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?
slide number 13
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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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slide number 20
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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.
slide number 21
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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 spanked on the bottoms of fractions-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 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.
slide number 22
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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 an 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? 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?
3 slide
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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!
4 slide
5 slide
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Kingdom of decimals 1st castle where you will learn about the history of decimals 2nd castle where you will learn Interesting Facts with decimal fractions 3rd castle, where you will be taught how to perform actions with decimal fractions 4th castle, where you will meet with exciting tasks that contain decimal fractions 5th castle, where you will be told a fairy tale about decimal fractions Exit the kingdom
6 slide
Description of the slide:
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.
7 slide
Description of the slide:
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.
8 slide
Description of the slide:
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:
9 slide
Description of the slide:
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
10 slide
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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.
11 slide
Description of the slide:
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!
12 slide
Description of the slide:
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?
13 slide
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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.
14 slide
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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?
15 slide
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Task 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?
16 slide
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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?
17 slide
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We will try to place these and many other tasks in the collection of tasks released by the 6th grade!
18 slide
Made by a student of the group T-1613 Kommusar L.V
INTRODUCTION
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 decimals...
- I don't understand anything! What? 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?
- 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 sang:
Decimals
We really need it.
What is a crooked letter?
Or is it a comma?
But what's with the comma?
Fairy Maya will tell us!
Here comes the fairy!
- Please to my kingdom! I found out that you do not know what decimal fractions are? And after visiting my castles, you will learn all about decimal fractions.
- We agree! - the girls said in unison and ended up in the kingdom.
Kingdom of decimals
1st castle where you will be introduced to the history of decimals
3rd lock, in which you will be taught how to perform actions with decimal fractions
5th castle, where they will tell you a fairy tale about decimal fractions
exit from
kingdoms
4 - th castle, where you will meet with exciting tasks in which there are decimal fractions
2nd castle in which you will learn interesting facts c decimals
From the history of decimals
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.
From the history of decimals
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.
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:
S. Stevin
0 I II III IV
3. 1 4 1 5
J. H. Beyer
1 415
A. Girard
It is interesting
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%.
Substance
dry
N 2
O 2
H 2 O
CO 2
Other
wet
It is interesting
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 by 92%
Cobalt at 0.5%
Nickel by 7.5%
The most accurate chemical analyzes of a huge number of meteorites that fell to Earth gave remarkable results. It turned out that in iron meteorites the percentage of iron, cobalt and nickel amazingly coincides with their content on our planet.
Verse about decimals
You can tell me a lot
What are decimal fractions
About what is possible at the end of the fractional part,
On 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 who has more
Of course, there will be more.
Well, if those parts are exactly equal,
What should I do, you tell me.
If two decimals have the same integer parts,
You look at the first of the mismatched digits,
And the one with more, of course, will have more.
Do you remember everything, you tell me?
How to add and subtract?
Remember the algorithm for adding or subtracting decimal fractions.
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 addition or subtraction first,
Paying no 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!
Where did decimals come from?
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.
Well, the old men and women sat all day in rocking chairs and read books, and sometimes spanked the bottoms of baby fractions 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 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.
Magic Decimals
The project was completed by a student
Inozemtseva Elizabeth
Mathematics teacher Voronenko I. E.
Introduction
On the most ordinary day after school, two best friends, fifth-grade students Katya and Ira, were doing their homework in mathematics. They opened the textbook and saw decimals...
I don't understand anything! What? These… like their… a… decimals. We did not pass them! - Ira was indignant.
Solve the problem with decimal fractions - Katya reads. - “In the spring they sowed 0.9 fields, and harvested only 0.6 fields. How much crop was not harvested from the field?
All the same, did they sow 0 or 9? - Ira asked.
Maybe you need to add 9 to 0? - Katya suggested.
No, we should probably choose 0 or 9 ourselves!
Katya agreed. And just as the girls wanted to write it down, the textbooks began to dance and sang:
Decimals
We really need.
What is a crooked letter?
Or is it a comma?
But what does the comma have to do with it, the fairy Maya will tell us!
Here comes the fairy!
Please to my kingdom! I found out that you don't know what decimals are?
And after visiting my castles, you will learn all about decimal fractions.
We agree! - the girls said in chorus and ended up in the kingdom.
Kingdom of decimals
The first castle where you will be introduced to the history of decimal fractions.
2nd castle, in which you will learn interesting facts about decimal fractions.
The 3rd castle, in which you will be taught how to perform actions with decimal fractions.
4th castle, where you will meet with exciting tasks that have decimal fractions.
5th castle, where you will be told a fairy tale about decimal fractions.
Lock 1 From the history of decimals
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 published the essay “Decimal Logistics” where he wrote: “... I noticed that technicians and artisans, when they measure any length, very rarely, in exceptional cases, express it in integers 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, i.e. minutes, seconds, etc., but it seems to me that their division into 60 parts is not as convenient as the division into 10,100 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.
Lock 2 Decimals in a person's life
We have heard a lot about air. Air is 99.96% composed of 3 gases: nitrogen, oxygen and argon.
Castle 3 Interesting
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 by 92%
Cobalt at 0.5%
Nickel by 7.5%
The most accurate chemical analyzes of a huge number of meteorites that fell to Earth gave remarkable results. It turned out that in iron meteorites the percentage of iron, cobalt and nickel coincides with their content on our planet.
Castle 4 Challenge
3.2 m of fabric was used for the coat, and 2.63 m for the suit. How much fabric did you use for the coat and suit together?
3.2+2.63=5.83 m.
