This is a sign for learning numbers from 1 to 100. The manual is suitable for children over 4 years old.

Those who are familiar with Montiasori learning probably have seen such a sign. She has many applications and now we will get acquainted with them.

The child must know the numbers to 10 well, before starting work with the table, as the account is up to 10 undergoing learning numbers up to 100 and higher.

With this table, the child will learn the names of the numbers up to 100; count to 100; sequence of numbers. You can also take it to read after 2, 3, 5, etc.

Table can be copied here

It consists of two parts (two third-party). Copy on one side of the sheet table with numbers up to 100, and with other empty cells where you can exercise. Laminating the table that the child could write on her markers and easily wipe.

How to use Table

	1. The table can be used to study numbers from 1 to 100. Starting with 1 and counting to 100. Initially, the parent / teacher shows how it is done. It is important that the child noticed the principle for which the numbers are repeated.
	2. On the laminated table, mark the same number. The child must say the next 3-4 numbers.
	3. Check several numbers. Ask a child to name their names. The second version of the exercise - the parent calls arbitrary numbers, and the child finds them and notes.
	4. Account after 5. The child considers 1,2,3,4,5 and notes the last (fifth) number.
	5. If you once again copy the pattern with numbers and cut it, you can make cards. They can be positioned in the table as you will see in the following lines In this case, the table is copied on the blue cardboard, which would be easily different from the white background table.
	6. Cards can be placed on the table and count - call a number by putting it a card. It helps the child to learn all the numbers. So it will exercise. Before that, it is important that the parent share cards of 10 (from 1 to 10; from 11 to 20; from 21 to 30, etc.). The child takes a card, puts it and calls the number.
	7. When the child has already advanced with the score, you can go to an empty table and place the cards there.
	8. Horizontal account or vertically. Maps place in a column or row and read all the numbers in order, whimping the pattern of their change - 6, 16, 26, 36, etc.
	9. Write a missing number. In an empty table, the parent writes arbitrary numbers. The child must add empty cells.

Back in the fourth grade I was interested in the question: "What are the numbers more than a billion? And why?". Since then, I have been looking for all the information on this issue and collected it on crumbs. But with the advent of Internet access, the search accelerated significantly. Now I imagine all the information I found, so that others can answer the question: "What are the big and very large numbers?".

A bit of history

Southern and Eastern Slavic nations for the recording of numbers used alphabetical numbering. Moreover, the Russian role has not all letters, but only those that are in the Greek alphabet. Above the letter, which denoted the number, was put a special "Title" icon. In this case, the numerical values \u200b\u200bof letters increased in the same order, in which letters followed in the Greek alphabet (the order of the letters of the Slavic alphabet was somewhat different).

In Russia, Slavic numbering has been preserved until the end of the 17th century. Under Peter I, the so-called "Arabic numbering", we use and now.

The names of the numbers also changed. For example, up to the 15th century, the number Twenty was designated as "two ten" (two dozen), but then decreased for faster pronunciation. Up to the 15th century, the number "Forty" was marked by the word "FIRST", and in the 15-16th centuries this word was supplanted by the word "forty", which initially marked the bag, which was placed on 40 squirrels or sobular skins. There are two options about the origin of the word "thousand": from the old title "Thick hundred" or from the modification of the Latin word Centum - "STO".

The name "Million" first appeared in Italy in 1500 and was formed by adding a magnifying suffix to the number "Mill" - a thousand (i.e. marked "a large thousand"), in Russian, it penetrated later, and before that the same meaning in Russian was marked by the number "Leodr". The word "billion" was used only from the time of the Franco-Prussa of War (1871), when the French had to pay Germany in 5,000,000,000 francs. Like "Million" the word "billion" comes from the root of "thousand" with the addition of Italian magnifying suffix. In Germany and America, for some time under the word "billion" implied the number of 100,000,000; This explains that the word billionaire in America began to be used before anyone from the rich has appeared 1000,000,000 dollars. In the old (XVIII century), the "arithmetic" of Magnitsky, the table of the names of the numbers brought to the "quadrillion" (10 ^ 24, by system through 6 discharges). Perelman Ya.I. In the book "Entertaining arithmetic", the names of large numbers of that time are given somewhat different from today: septylon (10 ^ 42), Occlicon (10 ^ 48), nonalone (10 ^ 54), decalon (10 ^ 60), Endecalon (10 ^ 66), Dodecalon (10 ^ 72) and it is written that "Next names are not available."

Principles of building titles and list of large numbers

All the names of large numbers are built quite simple: at the beginning there is a Latin sequence numerical, and at the end, suffix -illion is added to it. The exception is the name "Million" which is the name of the number of a thousand (MILLE) and the magnifying suffix -illion. In the world there are two main types of large numbers:
system 3x + 3 (where X - Latin sequence is numerical) - This system is used in Russia, France, USA, Canada, Italy, Turkey, Brazil, Greece
and system 6x (where X - Latin sequence is numerical) - this system is most common in the world (for example: Spain, Germany, Hungary, Portugal, Poland, Czech Republic, Sweden, Denmark, Finland). In it, the missing intermediate 6x + 3 end with the -illiard suffix (from it we borrowed a billion, which is also called Billion).

The general list of the numbers used in Russia is below:

...
• 10 100 - Gugol (number came up with a 9-year-old nephew of American mathematics Edward Casner)
• 10 123 - Quadragintillion (QuadragnTa, XL)
• 10 153 - Quinquaginta, L)
• 10 183 - Sexagintillion (Sexaginta, LX)
• 10 213 - Septuaginta, LXX)
• 10 243 - Oktogintillion (Octoginta, LXXX)
• 10 273 - Nonagintillion (Nonaginta, XC)
• 10 303 - Centur (C)

Further names can be obtained either direct, or in reverse Latin numerical order (as proper, not known):

• 10 306 - Angentillion or Centunillion
• 10 309 - Duocenteillion or centindollion
• 10 312 - Tirettyllion or Centrillion
• 10 315 - Quartercertillion or Cenkvadrillion
• 10 402 - Ferrigintantyaltyillion or Centraletrigintillion

I believe that the most correct will be the second version of writing, as it is more complies with the construction of numeral in Latin and avoids two-sensitivity (for example, among the first spelling, and 10 903 and 10 312).

Large numbers name systems

There are two numbers name systems - American and European (English).

In the American system, all the names of large numbers are built like this: at the beginning there is a Latin sequence numerical, and at the end of the suffix "ILRION" is added to it. The exception is the name "Million", which is the name of the number of a thousand (lat. Mille) and the magnifying suffix "Illion". So the numbers are trillion, quadrillion, quintillion, sextillion, etc. The American system is used in the USA, Canada, France and Russia. The number of zeros among the number recorded through the American system is determined by the formula 3 · x + 3 (where X is Latin numerical).

European (English) Name System is most common in the world. She enjoyed, for example, in the UK and Spain, as well as in most former English and Spanish colonies. The names of the numbers in this system are built as follows: the "Illion" suffix is \u200b\u200badded to the Latin numerical, the name of the next number (1,000 times greater) is formed from the same Latin numerical, but with the suffix "Illyde". That is, after a trillion in this system, trilliard goes, and only then the quadrillion followed by a quadrilliard, etc., the number of zeros, which recorded on the European system and the ending the "Ilion" suffix is \u200b\u200bdetermined by the formula 6 · x + 3 (where X is a Latin numerical) and according to the formula 6 · X + 6 for the numbers ending on the "Illyde". In some countries using the American system, for example, in Russia, Turkey, Italy, instead of the word "Billion" is used by the word "billion".

Both systems come from France. French physicist and mathematician Nicolas Shoche (Nicolas Chuquet) came up with the words "Billion" (byllion) and "Trillion" (Tryllion) and used them to designate numbers 10 12 and 10 18, respectively, which served as the basis of the European system.

But some French mathematicians in the XVII century used the words "Billion" and "Trillion" for numbers 10 9 and 10 12, respectively. This naming system has strengthened in France and in America, and began to be called the American, and the initial shock system continued to be used in the UK and Germany. France in 1948 returned to the shock system (i.e. European).

In recent years, the American system displaces European, partly in the UK and so far in the rest of European countries. Basically, this is due to the fact that Americans in financial transactions insist that 1,000,000,000 dollars need to be called billion dollars. In 1974, the Government of Prime Minister Harold Wilson announced that in official reports and statistics of Great Britain, the word Billion would be denoted 10 9, and not 10 12.

12 - Dozen (from FR. Douzaine or IT. Dozzina, which in turn occurred from Lat. Duodecim.)
Measure of the vulgar account of homogeneous subjects. Widely applied before the introduction of the metric system. For example, a dozen scarves, a dozen forks. 12 dozen make up Gross. For the first time in Russian, the word "dozen" is mentioned since 1720. It was originally used by sailors.

13 - Baker's dozen

The number is considered unfortunate. In many Western hotels there are no rooms with number 13, and in office buildings of the 13th floors. In the opera theaters of Italy, there are no places with this number. Almost on all ships after the 12th cabin immediately 14th.

144 - Gross - "big dozen" (from him. GRO? - Big)

Measure account equal to 12 dozens. Usually applied with the score of small haberdashery and stationery - pencils, buttons, painting peeks, etc. A dozen of Grossov is a mass.

1728 - Weight

Mass (statute) - measure of the score, equal to a dozen of grossov, i.e. 144 * 12 \u003d 1728 pieces. Widely applied before the introduction of the metric system.

666 or 616 - Number of beast

A special number mentioned in the Bible (KN. Revelations 13:18, 14: 2). It is assumed that due to the assignment of a numerical value, the letters of ancient alphabets, this number may mean any name or concept, the sum of the numerical values \u200b\u200bof the letters of which is 666. Such words can be: "Laetinos" (means in Greek everything Latin; proposed by Jerome ), "Nero Caesar", "Bonaparte" and even "Martin Luther". In some manuscripts, the beast is read as 616.

Miriada - the word is outdated and practically not used, but the word "Miriada" is widely used - (astronomer.), Which means countless, the intimate set of something.

Miriad was the largest number for which the ancient Greeks had a name. However, in the work of "Psammit" ("Calculustion of Peschin"), Archimedes showed how to systematically build and call arbitrarily large numbers. All numbers from 1 to Miriad (10,000) Archimedes called the first numbers, Miriad Miriad (10 8), he called the number of the numbers of the second (Dimiriad), Miriad Miriad of the second numbers (10 16), he called the unit of the number of third (trimyrium), and so on .

10 000 - dark
100 000 - legion
1 000 000 - leodr
10 000 000 - raven or Vran
100 000 000 - deck

Ancient Slavs also loved big numbers to be able to count to a billion. Moreover, such a score was called the "Small Account". In some manuscripts, the authors were also considered "the Great Account", reaching the number of 10 50. About the numbers more than 10 50 said: "And more than one to bear the human mind of understanding." The names used in the "Small Account" were transferred to the "Great Account", but with another meaning. So, darkness meant not 10,000, but a million, legion - darkness (million million); Leodr - Legion of the Legions - 10 24, then it was said - ten Leods, one hundred leodrov, ..., and, finally, one hundred thousand tops Leodrov - 10 47; Leodr Leodrov -10 48 was called raven and, finally, a deck -10 49.

10 140 - Asankheyi am (from whale. Asani - innumerable)

Mentioned in the famous Buddhist treatise Jaina-Sutra relating to 100 g. BC. It is believed that this number is equal to the number of space cycles required to gain nirvana.

Gugol. (from English. googol) - 10 100 , that is, a unit with a hundred zeros.

About "Google" for the first time wrote in 1938 in the article "New Names in Mathematics" in the January issue of Scripta Mathematica magazine American mathematician Edward Kasner (Edward Kasner). According to him, to call "Gugol" a large number suggested his nine-year-old nephew Milton Sirotta (Milton Sirotta). Well-known this number was due to the search engine named after him Google . Note that " Google" - this is trademark, but googol - number.

Googolplex (English GOOGOLPLEX) 10 10 100 - 10 to the degree of googol.

The number also invented by Castner with his nephew and meaning a unit with google zeros, that is, 10 to the extent of Google. Here's how Kasner himself describes this "Opening":

Words of Wisdom Are Spoken by Children At Least Asiss AS by Scientists. The Name "Googol" Was Invented by A Child (Dr. Kasner \\ "S Nine-Year-Old Nephew) Who Was Asked to Think Up a Name for a Very Big Number, Namely, 1 With a Hundred Zeros After IT. He Was Very Certain That This Number Was Not Infinite, And Theraefore Equally Certain That It Had to Have a Name. At the Same Time That He Suggested "Googol" HE GAVE A NAME FOR A STILL LARGER NUMBER: "GOOGOLPLEX." A GOOGOLPLEX IS MUCH LARGER Than A Googol, But Is Still Finite, As The Inventor of The Name Was Quick to Point Out.

Mathematics And the Imagination (1940) by Kasner and James R. Newman.

Number of Skusza (Skewes` NUMBER) - SK 1 E E E 79 - means E to the degree E to the degree E to degree 79.

J. Skews was suggested in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) In the proof of Riman's hypothesis concerning prime numbers. Later, Riele (Te Riele, HJJ "On the Sign of the Difference P (x) -li (X)." Math. Comput. 48, 323-328, 1987) reduced the number of Skusza to EE 27/4, which is approximately equal 8,185 10 370.

It was introduced by J. Skusom in the same article for the designation of the number, to which the Hypothesis of Riman is not valid. SK 2 is 10 10 10 10 3.

As you understand, the more degrees, the harder it is to understand which of the numbers is more. For example, looking at the number of Skusz, without special calculations, it is almost impossible to understand which of these two numbers is more. Thus, for super-high numbers, it becomes inconvenient to use degrees. Moreover, you can come up with such numbers (and they are already invented), when the degrees are simply not climbed into the page. Yes, that on the page! They will not fit, even in a book, the size of the whole Universe!

In this case, the question arises how to record them. The problem, as you understand, are solvable, and mathematics have developed several principles for recording such numbers. True, every mathematician who asked this problem came up with his way of recording, which led to the existence of several not related to each other, methods for recording numbers - these are notations of Knuta, Conway, Steinhause, etc.

Notation Hugo Stenhause (H. Steinhaus. Mathematical Snapshots, 3rd Edn. 1983) is pretty simple. Steinhauses (Shttoihaus) offered to record large numbers inside the geometric figures - a triangle, square and a circle.

Steinhauses came up with super-large numbers and called the number 2 in the circle - Mega, 3 in a circle - Medzon, and the number 10 in the circle - Megiston.

Mathematician Leo Moser The notation of the wallhause, which was limited to the fact that if it was required to record numbers a lot more Megiston, difficulties and inconvenience arose, since it had to draw a lot of circles one inside the other. Moser suggested not circles after squares, and pentagons, then hexagons and so on. He also offered a formal entry for these polygons so that the numbers can be recorded without drawing complex drawings. The notation of Moser looks like this:

• "n triangle" \u003d nn \u003d n.
• "N in a square" \u003d n \u003d "n in n triangles" \u003d nn.
• "N in a pentagon" \u003d n \u003d "n in n squares" \u003d Nn.
• n \u003d "n in n k-squares" \u003d n [k] n.

In the notation of Moser, Steinhouse Mega is recorded as 2, and Megstone as 10. Leo Moser offered to call a polygon with the number of sides of equal mega - magagon. As well as offered the number "2 in the megagon", that is, 2. This number became known as musor (Moser`s Number) or just like Moser. But the number of Mosel is not the largest number.

The largest number ever used in mathematical proof is the limit value known as graham number (Graham`s Number), first used in 1977 in the proof of one assessment in the Ramsey theory. It is associated with bichromatic hypercubes and cannot be expressed without a special 64-level system of special mathematical symbols introduced by D. Knutom in 1976.

In the names of the Arab numbers, each digit belongs to its discharge, and every three digits form a class. Thus, the last figure in the number indicates the number of units in it and is called, respectively, the discharge of units. The next, second from the end, the figure refers to dozens (discharge of tens), and the third from the end of the figure indicates the number of hundreds in the number - the discharge of hundreds. Further discharges are also repeated in turns in each class, denoting already units, dozens and hundreds in classes of thousands of millions, and so on. If the number is small and there are no numbers of tens or hundreds in it, it is customary to take them for zero. Classes are grouping numbers in three numbers, often in computing devices or records between classes, the point or space is set to visually divide them. This is done to simplify the reading of large numbers. Each class has its name: the first three digits are the class of units, then there is a class of thousands, then millions, billions (or billion) and so on.

Since we use a decimal calculus system, the main unit of measurement of quantity is a dozen, or 10 1. Accordingly, with an increase in the number of digits among the number, the number of tens 10 2, 10 3, 10 4, etc. increases. Knowing the number of dozens can be easily determined by the class and the discharge of the number, for example, 10 16 are tens of quadrillion, and 3 × 10 16 is three tens of quadrillion. The decomposition of numbers to decimal components occurs in the following way - each digit is displayed in a separate term, multiplied by the desired coefficient 10 N, where N is the position of the number on the expense from left to right.
For example: 253 981 \u003d 2 × 10 6 + 5 × 10 5 + 3 × 10 4 + 9 × 10 3 + 8 × 10 2 + 1 × 10 1

Also, the degree of number 10 is also used in writing decimal fractions: 10 (-1) is 0.1 or one tenth. Similarly, with the previous paragraph, it is possible to decompose the decimal number, n in this case will indicate the position of the filter number on the right to the left, for example: 0.347629 \u003d 3 × 10 (-1) + 4 × 10 (-2) + 7 × 10 (-3) + 6 × 10 (-4) + 2 × 10 (-5) + 9 × 10 (-6 )

The names of decimal numbers. Decimal numbers are read by the last category of numbers after a comma, for example, 0.325 - three hundred twenty-five thousandths, where thousandth is the rank of last digit 5.

Table names of large numbers, discharges and classes

It is known that numbers endless set And only a few have its own names, because most numbers received names consisting of small numbers. The greatest numbers need to be somehow denoted.

"Short" and "Long" scale

Used today the names of the number began to receive fifteenth century, Then the Italians first used the word million, having a "big thousand", Bimillion (million in square) and trimillion (million in Cuba).

This system described the Frenchman in his monograph Nicolas Shyuk, He recommended to use the numeral Latin language, adding a flexion "-Lion" to them, so Bimillion became a Billion, and trimillion trillion and so on.

But according to the proposed number of the number between a million and Billion, he called "thousands of millions". With such graduation it was not comfortable to work and in 1549, French Jacques Pelet I advised the numbers in the specified gap, call again using Latin consoles, while introducing another ending - "-lilliard".

So 109 got the name billion, 1015 - Billiard, 1021 - trilliard.

Gradually, this system began to use in Europe. But some scientists confused the names of numbers, it created a paradox when the words of Billion and a billion became synonymous. Subsequently, the United States was created in the USA. According to him, the construction of the name is carried out in the same way, but only numbers differ.

The former system continued to be applied in the UK, because it was named BritishAlthough it was originally created by the French. But from the seventies of the last century, the United Kingdom also began to apply the system.

Therefore, to avoid confusion created by American scientists. Concept, it is customary to refer short scale, while initial French-British - long scale.

A short scale has been active in the USA, Canada, Great Britain, Greece, Romania, Brazil. In Russia, it is also in the go, only with one difference - the number 109 is traditionally referred to as a billion. But the French-British version was preferred in a variety of other countries.

In order to designate the numbers, the big rather than Decillion, scientists decided to unite several Latin prefixes, so were called Undecillion, Quarterdecillion and others. If you use schuke system, That according to it, the gigantic numbers will acquire the names of "Vigintillion", "Centillion" and "Milleillion" (103003), respectively, according to a long scale, such a number will receive the name "Milleilliard" (106003).

Numbers with unique names

Many numbers got the name without binding to various systems and parts of words. These numbers a lot, for example, it pi", dozen, as well as numbers more than a million.

IN Ancient Russia A numerical system has long been used. Hundreds of thousands indicated the word Legion, Million - called Leodrome, tens of millions were crow, hundreds of millions were called a deck. It was a "small account", but the "Great Account" used the same words, that's only the meaning in them was investing other, for example, Leodr could mean Legion Legion (1024), and the deck was already ten raven (1096).

It happened that the names came up with children, so, Mathematics Edward Kesnera filed an idea young Milton Siretttaoffered to give a name with a hundred zeros (10100) just "Gugol" (GOOGOL). This number received the greatest publicity in the nineties of the twentieth century, when in his honor was called Google search engine. Also, the boy suggested the name "Googloplex", the number having the Gugol Nole.

But Claude Shannon in the middle of the twentieth century, assessing the moves in the chess game, calculated that there are 10118, now it is "Shannon Number".

In the old work of Buddhists "Jain-Sutra"Almost twenty-two-centuries ago, the number "Asankhai" (10140) is noted, it is so much space cycles, according to Buddhists, it is necessary to gain a nirvana.

Stanley Skews described large quantities, so "The first number of Skusza", Equal 10108,85.1033, and the "second number of Skusza" is still impressive and equals 1010101000.

Notation

Of course, depending on the number of degrees of the compounds contained, becomes the problematic problem in fixing it on the letter, and reading, the boss bases. Some numbers cannot be placed on several pages, therefore mathematics invented notations to fix large numbers.

It is necessary to take into account, they all differ, at the heart of each of their principles of fixation. Among those worth mentioning notation Steingegause, whip.

However, the largest number - "Graham Number" applied Ronald Gram in 1977 When conducting mathematical calculations, and this is the number G64.