17 digit number name. Big numbers have big names

In the names of Arabic numbers, each digit belongs to its category, and every three digits form a class. Thus, the last digit in a number indicates the number of units in it and is called, accordingly, the place of units. The next, second from the end, digit indicates tens (the tens digit), and the third digit from the end indicates the number of hundreds in the number - the hundreds digit. Further, the digits are repeated in the same way in turn in each class, denoting units, tens and hundreds in the classes of thousands, millions, and so on. If the number is small and does not contain a tens or hundreds digit, it is customary to take them as zero. Classes group numbers in numbers of three, often in computing devices or records a period or space is placed between classes to visually separate them. This is done to make it easier to read large numbers. Each class has its own name: the first three digits are the class of units, followed by the class of thousands, then millions, billions (or billions), and so on.

Since we use the decimal system, the basic unit of quantity is the ten, or 10 1 . Accordingly, with an increase in the number of digits in a number, the number of tens of 10 2, 10 3, 10 4, etc. also increases. Knowing the number of tens, you can easily determine the class and category of the number, for example, 10 16 is tens of quadrillions, and 3 × 10 16 is three tens of quadrillions. The decomposition of numbers into decimal components occurs as follows - each digit is displayed in a separate term, multiplied by the required coefficient 10 n, where n is the position of the digit in the count from left to right.
For example: 253 981=2×10 6 +5×10 5 +3×10 4 +9×10 3 +8×10 2 +1×10 1

Also, the power of 10 is also used in writing decimals: 10 (-1) is 0.1 or one tenth. Similarly with the previous paragraph, a decimal number can also be decomposed, in which case n will indicate the position of the digit from the comma from right to left, for example: 0.347629= 3x10 (-1) +4x10 (-2) +7x10 (-3) +6x10 (-4) +2x10 (-5) +9x10 (-6) )

Names of decimal numbers. Decimal numbers are read by the last digit after the decimal point, for example 0.325 - three hundred and twenty-five thousandths, where thousandths are the digit of the last digit 5.

Table of names of large numbers, digits and classes

1st class unit	1st unit digit 2nd place ten 3rd rank hundreds	1 = 10 0 10 = 10 1 100 = 10 2
2nd class thousand	1st digit units of thousands 2nd digit tens of thousands 3rd rank hundreds of thousands	1 000 = 10 3 10 000 = 10 4 100 000 = 10 5
3rd grade millions	1st digit units million 2nd digit tens of millions 3rd digit hundreds of millions	1 000 000 = 10 6 10 000 000 = 10 7 100 000 000 = 10 8
4th grade billions	1st digit units billion 2nd digit tens of billions 3rd digit hundreds of billions	1 000 000 000 = 10 9 10 000 000 000 = 10 10 100 000 000 000 = 10 11
5th grade trillions	1st digit trillion units 2nd digit tens of trillions 3rd digit hundred trillion	1 000 000 000 000 = 10 12 10 000 000 000 000 = 10 13 100 000 000 000 000 = 10 14
6th grade quadrillions	1st digit quadrillion units 2nd digit tens of quadrillions 3rd digit tens of quadrillions	1 000 000 000 000 000 = 10 15 10 000 000 000 000 000 = 10 16 100 000 000 000 000 000 = 10 17
7th grade quintillions	1st digit units of quintillions 2nd digit tens of quintillions 3rd rank hundred quintillion	1 000 000 000 000 000 000 = 10 18 10 000 000 000 000 000 000 = 10 19 100 000 000 000 000 000 000 = 10 20
8th grade sextillions	1st digit sextillion units 2nd digit tens of sextillions 3rd rank hundred sextillions	1 000 000 000 000 000 000 000 = 10 21 10 000 000 000 000 000 000 000 = 10 22 1 00 000 000 000 000 000 000 000 = 10 23
9th grade septillion	1st digit units of septillion 2nd digit tens of septillions 3rd rank hundred septillion	1 000 000 000 000 000 000 000 000 = 10 24 10 000 000 000 000 000 000 000 000 = 10 25 100 000 000 000 000 000 000 000 000 = 10 26
10th class octillion	1st digit octillion units 2nd digit ten octillion 3rd rank hundred octillion	1 000 000 000 000 000 000 000 000 000 = 10 27 10 000 000 000 000 000 000 000 000 000 = 10 28 100 000 000 000 000 000 000 000 000 000 = 10 29

Once in childhood, we learned to count to ten, then to a hundred, then to a thousand. So what is the biggest number you know? A thousand, a million, a billion, a trillion ... And then? Petallion, someone will say, will be wrong, because he confuses the SI prefix with a completely different concept.

In fact, the question is not as simple as it seems at first glance. First, we are talking about naming the names of the powers of a thousand. And here, the first nuance that many people know from American films is that they call our billion a billion.

Further more, there are two types of scales - long and short. In our country, a short scale is used. In this scale, at each step, the mantis increases by three orders of magnitude, i.e. multiply by a thousand - a thousand 10 3, a million 10 6, a billion / billion 10 9, a trillion (10 12). In the long scale, after a billion 10 9 comes a billion 10 12, and in the future the mantisa already increases by six orders of magnitude, and the next number, which is called a trillion, already stands for 10 18.

But back to our native scale. Want to know what comes after a trillion? Please:

10 3 thousand
10 6 million
10 9 billion
10 12 trillion
10 15 quadrillion
10 18 quintillion
10 21 sextillion
10 24 septillion
10 27 octillion
10 30 nonillion
10 33 decillion
10 36 undecillion
10 39 dodecillion
10 42 tredecillion
10 45 quattuordecillion
10 48 quindecillion
10 51 sedecillion
10 54 septdecillion
10 57 duodevigintillion
10 60 undevigintillion
10 63 vigintillion
10 66 anvigintillion
10 69 duovigintillion
10 72 trevigintillion
10 75 quattorvigintillion
10 78 quinvintillion
10 81 sexwigintillion
10 84 septemvigintillion
10 87 octovigintillion
10 90 novemvigintillion
10 93 trigintillion
10 96 antirigintillion

On this number, our short scale does not stand up, and in the future, the mantissa increases progressively.

10 100 googol
10 123 quadragintillion
10 153 quinquagintillion
10,183 sexagintillion
10 213 septuagintillion
10,243 octogintillion
10,273 nonagintillion
10 303 centillion
10 306 centunillion
10 309 centduollion
10 312 centtrillion
10 315 centquadrillion
10 402 centtretrigintillion
10,603 decentillion
10 903 trecentillion
10 1203 quadringentillion
10 1503 quingentillion
10 1803 sescentillion
10 2103 septingentillion
10 2403 octingentillion
10 2703 nongentillion
10 3003 million
10 6003 duomillion
10 9003 tremillion
10 3000003 miamimiliaillion
10 6000003 duomyamimiliaillion
10 10 100 googolplex
10 3×n+3 zillion

googol(from the English googol) - a number, in the decimal number system, represented by a unit with 100 zeros:
10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
In 1938, the American mathematician Edward Kasner (Edward Kasner, 1878-1955) was walking in the park with his two nephews and discussing large numbers with them. During the conversation, we talked about a number with one hundred zeros, which did not have its own name. One of his nephews, nine-year-old Milton Sirotta, suggested calling this number "googol". In 1940, Edward Kasner, together with James Newman, wrote the popular science book "Mathematics and Imagination" ("New Names in Mathematics"), where he taught mathematics lovers about the googol number.
The term "googol" has no serious theoretical and practical significance. Kasner proposed it to illustrate the difference between an unimaginably large number and infinity, and for this purpose the term is sometimes used in the teaching of mathematics.

Googolplex(from the English googolplex) - a number represented by a unit with a googol of zeros. Like googol, the term googolplex was coined by American mathematician Edward Kasner and his nephew Milton Sirotta.
The number of googols is greater than the number of all particles in the part of the universe known to us, which ranges from 1079 to 1081. Thus, the number of googolplexes, consisting of (googol + 1) digits, cannot be written in the classical “decimal” form, even if all matter in the known turn parts of the universe into paper and ink or into computer disk space.

Zillion(eng. zillion) is a common name for very large numbers.

This term does not have a strict mathematical definition. In 1996, Conway (English J. H. Conway) and Guy (English R. K. Guy) in their book English. The Book of Numbers defined a zillion of the nth power as 10 3×n+3 for the short scale number naming system.

As a child, I was tormented by the question of what is the largest number, and I plagued almost everyone with this stupid question. Having learned the number one million, I asked if there was a number greater than a million. Billion? And more than a billion? Trillion? And more than a trillion? Finally, someone smart was found who explained to me that the question is stupid, since it is enough just to add one to the largest number, and it turns out that it has never been the largest, since there are even larger numbers.

And now, after many years, I decided to ask another question, namely: What is the largest number that has its own name? Fortunately, now there is an Internet and you can puzzle them with patient search engines that will not call my questions idiotic ;-). Actually, this is what I did, and here's what I found out as a result.

Number	Latin name	Russian prefix
1	unus	en-
2	duo	duo-
3	tres	three-
4	quattuor	quadri-
5	quinque	quinti-
6	sex	sexty
7	September	septi-
8	octo	octi-
9	novem	noni-
10	decem	deci-

There are two systems for naming numbers - American and English.

The American system is built quite simply. All names of large numbers are built like this: at the beginning there is a Latin ordinal number, and at the end the suffix -million is added to it. The exception is the name "million" which is the name of the number one thousand (lat. mille) and the magnifying suffix -million (see table). So the numbers are obtained - trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion and decillion. The American system is used in the USA, Canada, France and Russia. You can find out the number of zeros in a number written in the American system using the simple formula 3 x + 3 (where x is a Latin numeral).

The English naming system is the most common in the world. It is used, for example, in Great Britain and Spain, as well as in most of the former English and Spanish colonies. The names of numbers in this system are built like this: like this: a suffix -million is added to the Latin numeral, the next number (1000 times larger) is built according to the principle - the same Latin numeral, but the suffix is -billion. That is, after a trillion in the English system comes a trillion, and only then a quadrillion, followed by a quadrillion, and so on. Thus, a quadrillion according to the English and American systems are completely different numbers! You can find out the number of zeros in a number written in the English system and ending with the suffix -million using the formula 6 x + 3 (where x is a Latin numeral) and using the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system into the Russian language, which, nevertheless, would be more correct to call it the way the Americans call it - a billion, since we have adopted the American system. But who in our country does something according to the rules! ;-) By the way, sometimes the word trilliard is also used in Russian (you can see for yourself by running a search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.

In addition to numbers written using Latin prefixes in the American or English system, the so-called off-system numbers are also known, i.e. numbers that have their own names without any Latin prefixes. There are several such numbers, but I will talk about them in more detail a little later.

Let's go back to writing using Latin numerals. It would seem that they can write numbers to infinity, but this is not entirely true. Now I will explain why. First, let's see how the numbers from 1 to 10 33 are called:

Name	Number
Unit	10 0
Ten	10 1
Hundred	10 2
One thousand	10 3
Million	10 6
Billion	10 9
Trillion	10 12
quadrillion	10 15
Quintillion	10 18
Sextillion	10 21
Septillion	10 24
Octillion	10 27
Quintillion	10 30
Decillion	10 33

And so, now the question arises, what next. What is a decillion? In principle, it is possible, of course, by combining prefixes to generate such monsters as: andecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion and novemdecillion, but these will already be compound names, and we were interested in our own names numbers. Therefore, according to this system, in addition to the above, you can still get only three proper names - vigintillion (from lat. viginti- twenty), centillion (from lat. percent- one hundred) and a million (from lat. mille- one thousand). The Romans did not have more than a thousand proper names for numbers (all numbers over a thousand were composite). For example, a million (1,000,000) Romans called centena milia i.e. ten hundred thousand. And now, actually, the table:

Thus, according to a similar system, numbers greater than 10 3003, which would have its own, non-compound name, cannot be obtained! But nevertheless, numbers greater than a million are known - these are the same off-system numbers. Finally, let's talk about them.

Name	Number
myriad	10 4
googol	10 100
Asankheyya	10 140
Googolplex	10 10 100
Skuse's second number	10 10 10 1000
Mega	2 (in Moser notation)
Megiston	10 (in Moser notation)
Moser	2 (in Moser notation)
Graham number	G 63 (in Graham's notation)
Stasplex	G 100 (in Graham's notation)

The smallest such number is myriad(it is even in Dahl's dictionary), which means a hundred hundreds, that is, 10,000. True, this word is outdated and practically not used, but it is curious that the word "myriads" is widely used, which means not a certain number at all, but an innumerable, uncountable number of things. It is believed that the word myriad (English myriad) came to European languages from ancient Egypt.

googol(from the English googol) is the number ten to the hundredth power, that is, one with one hundred zeros. The "googol" was first written about in 1938 in the article "New Names in Mathematics" in the January issue of the journal Scripta Mathematica by the American mathematician Edward Kasner. According to him, his nine-year-old nephew Milton Sirotta suggested calling a large number "googol". This number became well-known thanks to the search engine named after him. Google. Note that "Google" is a trademark and googol is a number.

In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, there is a number asankhiya(from Chinese asentzi- incalculable), equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to gain nirvana.

Googolplex(English) googolplex) - a number also invented by Kasner with his nephew and meaning one with a googol of zeros, that is, 10 10 100. Here is how Kasner himself describes this "discovery":

Words of wisdom are spoken by children at least as often 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 therefore equally certain that it had to have a name. 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.

Even more than a googolplex number, Skewes' number was proposed by Skewes in 1933 (Skewes. J. London Math. soc. 8 , 277-283, 1933.) in proving the Riemann conjecture concerning primes. It means e to the extent e to the extent e to the power of 79, that is, e e e 79. Later, Riele (te Riele, H. J. J. "On the Sign of the Difference P(x)-Li(x)." Math. Comput. 48 , 323-328, 1987) reduced the Skewes number to e e 27/4 , which is approximately equal to 8.185 10 370 . It is clear that since the value of the Skewes number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to recall other non-natural numbers - the number pi, the number e, the Avogadro number, etc.

But it should be noted that there is a second Skewes number, which in mathematics is denoted as Sk 2 , which is even larger than the first Skewes number (Sk 1). Skuse's second number, was introduced by J. Skuse in the same article to denote the number up to which the Riemann hypothesis is valid. Sk 2 is equal to 10 10 10 10 3 , that is 10 10 10 1000 .

As you understand, the more degrees there are, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skewes numbers, without special calculations, it is almost impossible to understand which of these two numbers is larger. Thus, for superlarge numbers, it becomes inconvenient to use powers. Moreover, you can come up with such numbers (and they have already been invented) when the degrees of degrees simply do not fit on the page. Yes, what a page! They won't even fit into a book the size of the entire universe! In this case, the question arises how to write them down. The problem, as you understand, is solvable, and mathematicians have developed several principles for writing such numbers. True, every mathematician who asked this problem came up with his own way of writing, which led to the existence of several, unrelated, ways to write numbers - these are the notations of Knuth, Conway, Steinhouse, etc.

Consider the notation of Hugo Stenhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is quite simple. Steinhouse suggested writing large numbers inside geometric shapes - a triangle, a square and a circle:

Steinhouse came up with two new super-large numbers. He named a number Mega, and the number is Megiston.

The mathematician Leo Moser refined Stenhouse's notation, which was limited by the fact that if it was necessary to write numbers much larger than a megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested drawing not circles after squares, but pentagons, then hexagons, and so on. He also proposed a formal notation for these polygons, so that numbers could be written without drawing complex patterns. Moser notation looks like this:

Thus, according to Moser's notation, Steinhouse's mega is written as 2, and megiston as 10. In addition, Leo Moser suggested calling a polygon with the number of sides equal to mega - megagon. And he proposed the number "2 in Megagon", that is, 2. This number became known as the Moser's number or simply as moser.

But the moser is not the largest number. The largest number ever used in a mathematical proof is the limiting value known as Graham number(Graham "s number), first used in 1977 in the proof of one estimate in Ramsey theory. It is associated with bichromatic hypercubes and cannot be expressed without a special 64-level system of special mathematical symbols introduced by Knuth in 1976.

Unfortunately, the number written in the Knuth notation cannot be translated into the Moser notation. Therefore, this system will also have to be explained. In principle, there is nothing complicated in it either. Donald Knuth (yes, yes, this is the same Knuth who wrote The Art of Programming and created the TeX editor) came up with the concept of superpower, which he proposed to write with arrows pointing up:

In general, it looks like this:

I think that everything is clear, so let's get back to Graham's number. Graham proposed the so-called G-numbers:

The number G 63 began to be called Graham number(it is often denoted simply as G). This number is the largest known number in the world and is even listed in the Guinness Book of Records. And, here, that the Graham number is greater than the Moser number.

P.S. In order to bring great benefit to all mankind and become famous for centuries, I decided to invent and name the largest number myself. This number will be called stasplex and it is equal to the number G 100 . Memorize it, and when your children ask what is the largest number in the world, tell them that this number is called stasplex.

Update (4.09.2003): Thanks everyone for the comments. It turned out that when writing the text, I made several mistakes. I'll try to fix it now.

I made several mistakes at once, just mentioning Avogadro's number. First, several people have pointed out to me that 6.022 10 23 is actually the most natural number. And secondly, there is an opinion, and it seems to me true, that Avogadro's number is not a number at all in the proper, mathematical sense of the word, since it depends on the system of units. Now it is expressed in "mol -1", but if it is expressed, for example, in moles or something else, then it will be expressed in a completely different figure, but it will not stop being Avogadro's number at all.
10 000 - darkness
100,000 - legion
1,000,000 - leodre
10,000,000 - Raven or Raven
100 000 000 - deck
Interestingly, the ancient Slavs also loved large numbers, they knew how to count up to a billion. Moreover, they called such an account a “small account”. In some manuscripts, the authors also considered the "great count", which reached the number 10 50 . About numbers greater than 10 50 it was said: "And more than this to bear the human mind to understand." The names used in the "small account" were transferred to the "great account", but with a different meaning. So, darkness meant no longer 10,000, but a million, legion - the darkness of those (million millions); leodrus - a legion of legions (10 to 24 degrees), then it was said - ten leodres, a hundred leodres, ..., and, finally, a hundred thousand legions of leodres (10 to 47); leodr leodr (10 to 48) was called a raven and, finally, a deck (10 to 49).
The topic of national names of numbers can be expanded if we recall the Japanese system of naming numbers that I forgot, which is very different from the English and American systems (I will not draw hieroglyphs, if anyone is interested, then they are):
100-ichi
10 1 - jyuu
10 2 - hyaku
103-sen
104 - man
108-oku
10 12 - chou
10 16 - kei
10 20 - gai
10 24 - jyo
10 28 - jyou
10 32 - kou
10 36-kan
10 40 - sei
1044 - sai
1048 - goku
10 52 - gougasya
10 56 - asougi
10 60 - nayuta
1064 - fukashigi
10 68 - murioutaisuu
Regarding the numbers of Hugo Steinhaus (in Russia, for some reason, his name was translated as Hugo Steinhaus). botev assures that the idea of writing super-large numbers in the form of numbers in circles does not belong to Steinhouse, but to Daniil Kharms, who, long before him, published this idea in the article "Raising the Number". I also want to thank Evgeny Sklyarevsky, the author of the most interesting site on entertaining mathematics on the Russian-speaking Internet - Arbuz, for the information that Steinhouse came up with not only the numbers mega and megiston, but also proposed another number mezzanine, which is (in his notation) "circled 3".
Now for the number myriad or myrioi. There are different opinions about the origin of this number. Some believe that it originated in Egypt, while others believe that it was born only in ancient Greece. Be that as it may, in fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, and there were no names for numbers over ten thousand. However, in the note "Psammit" (i.e., the calculus of sand), Archimedes showed how one can systematically build and name arbitrarily large numbers. In particular, placing 10,000 (myriad) grains of sand in a poppy seed, he finds that in the Universe (a ball with a diameter of a myriad of Earth diameters) no more than 10 63 grains of sand would fit (in our notation). It is curious that modern calculations of the number of atoms in the visible universe lead to the number 10 67 (only a myriad times more). The names of the numbers Archimedes suggested are as follows:
1 myriad = 10 4 .
1 di-myriad = myriad myriad = 10 8 .
1 tri-myriad = di-myriad di-myriad = 10 16 .
1 tetra-myriad = three-myriad three-myriad = 10 32 .
etc.

If there are comments -

In everyday life, most people operate with fairly small numbers. Tens, hundreds, thousands, very rarely - millions, almost never - billions. Approximately such numbers are limited to the usual idea of \u200b\u200ba person about quantity or magnitude. Almost everyone has heard about trillions, but few have ever used them in any calculations.

What are giant numbers?

Meanwhile, the numbers denoting the powers of a thousand have been known to people for a long time. In Russia and many other countries, a simple and logical notation system is used:

One thousand;
Million;
Billion;
Trillion;
quadrillion;
Quintillion;
Sextillion;
Septillion;
Octillion;
Quintillion;
Decillion.

In this system, each next number is obtained by multiplying the previous one by a thousand. A billion is commonly referred to as a billion.

Many adults can accurately write such numbers as a million - 1,000,000 and a billion - 1,000,000,000. It’s already more difficult with a trillion, but almost everyone can handle it - 1,000,000,000,000. And then the territory unknown to many begins.

Getting to know the big numbers

However, there is nothing complicated, the main thing is to understand the system for the formation of large numbers and the principle of naming. As already mentioned, each next number exceeds the previous one by a thousand times. This means that in order to correctly write the next number in ascending order, you need to add three more zeros to the previous one. That is, a million has 6 zeros, a billion has 9, a trillion has 12, a quadrillion has 15, and a quintillion has 18.

You can also deal with the names if you wish. The word "million" comes from the Latin "mille", which means "more than a thousand". The following numbers were formed by adding the Latin words "bi" (two), "three" (three), "quadro" (four), etc.

Now let's try to imagine these numbers visually. Most people have a pretty good idea of the difference between a thousand and a million. Everyone understands that a million rubles is good, but a billion is more. Much more. Also, everyone has an idea that a trillion is something absolutely immense. But how much is a trillion more than a billion? How huge is it?

For many, beyond a billion, the concept of "the mind is incomprehensible" begins. Indeed, a billion kilometers or a trillion - the difference is not very big in the sense that such a distance still cannot be covered in a lifetime. A billion rubles or a trillion is also not very different, because you still can’t earn that kind of money in a lifetime. But let's count a little, connecting the fantasy.

Housing stock in Russia and four football fields as examples

For every person on earth, there is a land area measuring 100x200 meters. That's about four football fields. But if there are not 7 billion people, but seven trillion, then everyone will get only a piece of land 4x5 meters. Four football fields against the area of the front garden in front of the entrance - this is the ratio of a billion to a trillion.

In absolute terms, the picture is also impressive.

If you take a trillion bricks, you can build more than 30 million one-story houses with an area of 100 square meters. That is about 3 billion square meters of private development. This is comparable to the total housing stock of the Russian Federation.

If you build ten-story houses, you will get about 2.5 million houses, that is, 100 million two-three-room apartments, about 7 billion square meters of housing. This is 2.5 times more than the entire housing stock in Russia.

In a word, there will not be a trillion bricks in all of Russia.

One quadrillion student notebooks will cover the entire territory of Russia with a double layer. And one quintillion of the same notebooks will cover the entire land with a layer 40 centimeters thick. If you manage to get a sextillion notebooks, then the entire planet, including the oceans, will be under a layer 100 meters thick.

Count to a decillion

Let's count some more. For example, a matchbox magnified a thousand times would be the size of a sixteen-story building. An increase of a million times will give a "box", which is larger than St. Petersburg in area. Magnified a billion times, the boxes won't fit on our planet. On the contrary, the Earth will fit in such a "box" 25 times!

An increase in the box gives an increase in its volume. It will be almost impossible to imagine such volumes with a further increase. For ease of perception, let's try to increase not the object itself, but its quantity, and arrange the matchboxes in space. This will make it easier to navigate. A quintillion of boxes laid out in one row would stretch beyond the star α Centauri by 9 trillion kilometers.

Another thousandfold magnification (sextillion) will allow matchboxes lined up to block our entire Milky Way galaxy in the transverse direction. A septillion matchboxes would span 50 quintillion kilometers. Light can travel this distance in 5,260,000 years. And the boxes laid out in two rows would stretch to the Andromeda galaxy.

There are only three numbers left: octillion, nonillion and decillion. You have to exercise your imagination. An octillion of boxes forms a continuous line of 50 sextillion kilometers. That's over five billion light years. Not every telescope mounted on one edge of such an object would be able to see its opposite edge.

Do we count further? A nonillion matchboxes would fill the entire space of the part of the Universe known to mankind with an average density of 6 pieces per cubic meter. By earthly standards, it seems to be not very much - 36 matchboxes in the back of a standard Gazelle. But a nonillion matchboxes will have a mass billions of times greater than the mass of all material objects in the known universe combined.

Decillion. The magnitude, and rather even the majesty of this giant from the world of numbers, is hard to imagine. Just one example - six decillion boxes would no longer fit in the entire part of the universe accessible to mankind for observation.

Even more strikingly, the majesty of this number is visible if you do not multiply the number of boxes, but increase the object itself. A matchbox enlarged by a factor of a decillion would contain the entire known part of the universe 20 trillion times. It is impossible to even imagine such a thing.

Small calculations showed how huge the numbers known to mankind for several centuries are. In modern mathematics, numbers many times greater than a decillion are known, but they are used only in complex mathematical calculations. Only professional mathematicians have to deal with such numbers.

The most famous (and smallest) of these numbers is the googol, denoted by one followed by one hundred zeros. A googol is greater than the total number of elementary particles in the visible part of the Universe. This makes the googol an abstract number that has little practical use.

It is known that an infinite number of numbers and only a few have names of their own, for most numbers have been given names consisting of small numbers. The largest numbers must be denoted in some way.

"Short" and "long" scale

Number names used today began to receive in the fifteenth century, then the Italians first used the word million, meaning "big thousand", bimillion (million squared) and trimillion (million cubed).

This system was described in his monograph by the Frenchman Nicholas Shuquet, he recommended using Latin numerals, adding to them the inflection "-million", so bimillion became a billion, and three million became a trillion, and so on.

But according to the proposed system of numbers between a million and a billion, he called "a thousand millions." It was not comfortable to work with such a gradation and in 1549 the Frenchman Jacques Peletier advised to call the numbers that are in the specified interval, again using Latin prefixes, while introducing another ending - “-billion”.

So 109 was called a billion, 1015 - billiard, 1021 - trillion.

Gradually, this system began to be used in Europe. But some scientists confused the names of numbers, this created a paradox when the words billion and billion became synonymous. Subsequently, the United States created its own naming convention for large numbers. According to him, the construction of names is carried out in a similar way, but only the numbers differ.

The old system continued to be used in the UK, and therefore was called British, although it was originally created by the French. But since the seventies of the last century, Great Britain also began to apply the system.

Therefore, in order to avoid confusion, the concept created by American scientists is usually called short scale, while the original French-British - long scale.

The short scale has found active use in the USA, Canada, Great Britain, Greece, Romania, and Brazil. In Russia, it is also in use, with only one difference - the number 109 is traditionally called a billion. But the French-British version was preferred in many other countries.

In order to designate numbers larger than a decillion, scientists decided to combine several Latin prefixes, so the undecillion, quattordecillion and others were named. If you use Schuecke system, then according to it, giant numbers will acquire the names "vigintillion", "centillion" and "millionillion" (103003), respectively, according to the long scale, such a number will receive the name "millionillion" (106003).

Numbers with unique names

Many numbers were named without reference to various systems and parts of words. There are a lot of these numbers, for example, this Pi", a dozen, as well as numbers over a million.

AT Ancient Russia has long used its own numerical system. Hundreds of thousands were called legion, a million were called leodroms, tens of millions were crows, hundreds of millions were called decks. It was a “small account”, but the “great account” used the same words, only a different meaning was put into them, for example, leodr could mean a legion of legions (1024), and a deck could already mean ten ravens (1096).

It happened that children came up with names for numbers, for example, mathematician Edward Kasner was given the idea young Milton Sirotta, who proposed giving a name to a number with a hundred zeros (10100) simply googol. This number received the most publicity in the nineties of the twentieth century, when the Google search engine was named after him. The boy also suggested the name "Googleplex", a number that has a googol of zeros.

But Claude Shannon in the middle of the twentieth century, evaluating the moves in a chess game, calculated that there are 10118 of them, now it is "Shannon number".

In an old Buddhist work "Jaina Sutras", written almost twenty-two centuries ago, the number "asankheya" (10140) is noted, which is exactly how many cosmic cycles, according to Buddhists, it is necessary to achieve nirvana.

Stanley Skuse described large quantities, so "the first Skewes number", equal to 10108.85.1033, and the "second Skewes number" is even more impressive and equals 1010101000.

Notations

Of course, depending on the number of degrees contained in a number, it becomes problematic to fix it on writing, and even reading, error bases. some numbers cannot fit on multiple pages, so mathematicians have come up with notations to capture large numbers.

It is worth considering that they are all different, each has its own principle of fixation. Among these, it is worth mentioning notations by Steinghaus, Knuth.

However, the largest number, the Graham number, was used Ronald Graham in 1977 when doing mathematical calculations, and this number is G64.