Ascending table of numbers. The largest number in the world

Countless different numbers surround us every day. Surely many people wondered at least once what number is considered the largest. You can simply tell a child that this is a million, but adults are well aware that other numbers follow a million. For example, it is only necessary to add one to the number each time, and it will become more and more - this happens ad infinitum. But if you take apart the numbers that have names, you can find out what the largest number in the world is called.

The emergence of the names of numbers: what methods are used?

Today there are 2 systems according to which numbers are given names - American and English. The first is fairly straightforward, while the second is the most common around the world. American allows you to give names to large numbers like this: first, the ordinal number in Latin is indicated, and then the suffix "illion" is added (the exception here is a million, meaning a thousand). This system is used by the Americans, French, Canadians, and it is also used in our country.

English is widely used in England and Spain. According to it, the numbers are named as follows: the numeral in Latin is "plus" with the suffix "illion", and the next (a thousand times larger) number is "plus" "illiard". For example, first comes a trillion, followed by a trillion, followed by a quadrillion, and so on.

So, the same number in different systems can mean different things, for example, the American billion in the English system is called a billion.

Off-system numbers

In addition to numbers that are written according to known systems (above), there are also non-systemic ones. They have their own names, which do not include Latin prefixes.

You can start considering them with a number called a myriad. It is defined as one hundred hundreds (10000). But for its intended purpose, this word is not used, but is used as an indication of the innumerable. Even Dahl's dictionary will kindly provide a definition of such a number.

The next after the myriad is googol, denoting 10 to the power of 100. This name was first used in 1938 - by a mathematician from America E. Kasner, who noted that this name was invented by his nephew.

Google (search engine) got its name in honor of googol. Then 1-tsa with a googol of zeros (1010100) is a googolplex - Kasner also invented this name.

Even larger in comparison with the googolplex is the Skuse number (e to the e to the power of e79), proposed by Skuse in the proof of the Rimmann conjecture on primes (1933). There is another Skuse number, but it is applied when the Rimmann hypothesis is not valid. It is rather difficult to say which of them is more, especially when it comes to large degrees. However, this number, despite its "enormity", cannot be considered the most-most of all those that have their own names.

And the leader among the largest numbers in the world is the Graham number (G64). It was he who was used for the first time to carry out proofs in the field of mathematical science (1977).

When it comes to such a number, you need to know that you cannot do without a special 64-level system created by Knut - the reason for this is the connection of the number G with bichromatic hypercubes. The whip invented a superdegree, and in order to make it convenient to make her notes, he suggested using the up arrows. So we learned the name of the largest number in the world. It is worth noting that this G number got on the pages of the famous Book of Records.

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

And now, many years later, I decided to ask another question, namely: what is the largest number that has its own name? Fortunately, now there is an Internet and they can be puzzled by patient search engines that will not call my questions idiotic ;-). Actually, this is what I did, and this is what I found out as a result.

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

The American system is pretty simple. All the names of large numbers are constructed as follows: at the beginning there is a Latin ordinal number, and at the end the suffix-million is added to it. An exception is the name "million" which is the name of the number one thousand (lat. mille) and the increasing suffix-million (see table). This is how 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: so: the 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, there is a trillion, and only then a quadrillion, followed by a quadrillion, etc. Thus, a quadrillion in 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 by the formula 6 x + 3 (where x is a Latin numeral) and by the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system to the Russian language, which would still be more correct to call it as the Americans call it - a billion, since it is the American system that has been adopted in our country. But who in our country does something according to the rules! ;-) By the way, sometimes the word trillion 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 according to the American or English system, 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. Let me explain why. Let's first see how the numbers from 1 to 10 33 are called:

And so, now the question arises, what's next. What's behind the decillion? In principle, of course, 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, but we were interested in 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. centum- one hundred) and a million (from lat. mille- one thousand). The Romans did not have more than a thousand of their own names for numbers (all numbers over a thousand were composite). For example, the Romans called a million (1,000,000) decies centena milia, that is, "ten hundred thousand". And now, in fact, the table:

Thus, according to such a system, the number is greater than 10 3003, which would have its own, non-compound name, it is impossible to get! But nevertheless, numbers more than a million million are known - these are the very off-system numbers. Let's finally tell you about them.

The smallest such number is myriad(it is even in Dahl's dictionary), which means a hundred hundred, that is, 10,000. This word, however, is outdated and is practically not used, but it is curious that the word "myriad" is widely used, which does not mean a certain number at all, but an uncountable, uncountable set of things. It is believed that the word myriad came into 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. Googol was first written about in 1938 in the article "New Names in Mathematics" in the January issue of 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 of the Jaina Sutra, dating back to 100 BC, there is a number asankheya(from whale. asenci- uncountable) equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Googolplex(eng. googolplex) is a number also invented by Kasner with his nephew and means one with a googol of zeros, that is, 10 10 100. This 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. 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.

An even larger number than the googolplex, the Skewes "number, was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8 , 277-283, 1933.) in proving the Riemann conjecture concerning prime numbers. It means e to the extent e to the extent e to the 79th power, 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 8.185 10 370. It is clear that since the value of Skuse's 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 - pi, e, Avogadro's number, etc.

But it should be noted that there is a second Skuse number, which in mathematics is denoted as Sk 2, which is even greater than the first Skuse number (Sk 1). Second Skewes 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 there are in the number of degrees, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skuse numbers, without special calculations, it is almost impossible to understand which of these two numbers is greater. Thus, it becomes inconvenient to use powers for very large numbers. Moreover, you can think of 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 will not fit, even in 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 wondered about 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 Steinhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is pretty simple. Stein House proposed to write large numbers inside geometric shapes - a triangle, a square and a circle:

Steinhaus came up with two new super-large numbers. He called the 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 required to write numbers much larger than the megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested drawing not circles, but pentagons after the squares, then hexagons, and so on. He also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings. Moser's notation looks like this:

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

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

Unfortunately, the number written in Knuth's notation cannot be translated into the Moser system. Therefore, we will have to explain this system as well. In principle, there is nothing complicated about it either. Donald Knuth (yes, yes, this is the same Knuth who wrote "The Art of Programming" and created the TeX editor) invented the concept of superdegree, which he proposed to write down with arrows pointing up:

In general, it looks like this:

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

The number G 63 became known as Graham number(it is often denoted simply as G). This number is the largest known number in the world and is even included in the Guinness Book of Records. Ah, here's that Graham's number is greater than Moser's.

P.S. In order to bring great benefit to all mankind and become famous for centuries, I decided to come up with 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): Thank you all for the comments. It turned out that I made several mistakes while writing the text. I'll try to fix it now.

1. I made several mistakes at once by simply mentioning Avogadro's number. Firstly, several people pointed out to me that in fact 6.022 · 10 23 is the most natural number. And secondly, there is an opinion, and it seems to me correct, that Avogadro's number is not at all a number in the proper, mathematical sense of the word, since it depends on the system of units. Now it is expressed in "mole -1", but if you express it, for example, in moles or something else, it will be expressed in a completely different number, but this will not stop being Avogadro's number at all.
2. 10,000 - darkness
   100,000 - legion
   1,000,000 - leodr
   10,000,000 - a raven or a lie
   100,000,000 - deck
   Interestingly, the ancient Slavs also loved large numbers and knew how to count up to a billion. Moreover, they called such an account "small account". In some manuscripts, the authors also considered the "great score", reaching the number of 10 50. About numbers more than 10 50 it was said: "And the human mind cannot understand more than this." The names used in "small count" were carried over to "great count", but with a different meaning. So, darkness meant no longer 10,000, but a million, a legion meant darkness for those (a million million); leodr - legion of legions (10 to 24 degrees), then it was said - ten leodr, one hundred leodr, ..., and, finally, one hundred thousand leodr legion (10 to 47); leodr leodr (10 in 48) was called a raven and, finally, a deck (10 in 49).
3. The topic of national names for numbers can be expanded if we recall the forgotten Japanese system of naming numbers, which is very different from the English and American systems (I will not draw hieroglyphs, if someone is interested, they are):
   10 0 - ichi
   10 1 - jyuu
   10 2 - hyaku
   10 3 - sen
   10 4 - man
   10 8 - 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
   10 44 - sai
   10 48 - goku
   10 52 - gougasya
   10 56 - asougi
   10 60 - nayuta
   10 64 - fukashigi
   10 68 - muryoutaisuu
4. Concerning 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 belongs not to Steinhaus, but to Daniil Kharms, who published this idea for nothing 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-language Internet - Watermelon, for the information that Steinhaus came up with not only the mega and megiston numbers, but also suggested another number mezzon, equal (in its notation) to "3 in a circle".
5. Now about 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 reality, but the myriad gained fame thanks to the Greeks. Myriad was the name for 10,000, but there were no names for numbers over ten thousand. However, in the note "Psammit" (ie the calculus of sand), Archimedes showed how one can systematically construct 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 sphere with a diameter of a myriad of Earth's diameters) no more than 1063 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 (just a myriad of times more). Archimedes suggested the following names for numbers:
   1 myriad = 10 4.
   1 d-myriad = myriad of myriads = 10 8.
   1 three-myriad = di-myriad of di-myriads = 10 16.
   1 tetra-myriad = three-myriad three-myriad = 10 32.
   etc.

If there are any comments -

Many people are interested in questions about how large numbers are called and which number is the largest in the world. We will deal with these interesting questions in this article.

Story

The southern and eastern Slavic peoples used alphabetical numbering to write numbers, and only those letters that are in the Greek alphabet. A special “titlo” icon was placed above the letter that denoted the number. The numerical values ​​of the letters increased in the same order in which the letters followed in the Greek alphabet (in the Slavic alphabet, the order of the letters was slightly different). In Russia, Slavic numbering was preserved until the end of the 17th century, and under Peter I they switched to “Arabic numbering”, which we still use today.

The names of the numbers have changed too. So, until the 15th century, the number “twenty” was designated as “two ten” (two dozen), and then it was reduced for a faster pronunciation. Until the 15th century, the number 40 was called “fourty”, then it was supplanted by the word “forty”, originally denoting a bag containing 40 squirrel or sable skins. The name “million” appeared in Italy in 1500. It was formed by adding a magnifying suffix to the number millet (thousand). Later, this name came to the Russian language.

In the old (XVIII century) "Arithmetic" by Magnitsky, a table of the names of numbers is given, brought to "quadrillion" (10 ^ 24, according to the system after 6 digits). Perelman Ya.I. in the book "Entertaining arithmetic" the names of large numbers of that time are given, somewhat different from those of today: septillion (10 ^ 42), octalion (10 ^ 48), nonalion (10 ^ 54), decallion (10 ^ 60), endecalion (10 ^ 66), dodecalion (10 ^ 72) and it is written that "there are no further names."

Methods for constructing names of large numbers

There are 2 main ways of naming large numbers:

• American system which is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are built quite simply: first comes the Latin ordinal number, and the suffix “-million” is added to it at the end. Exceptions are the number “million”, which is the name of the number thousand (mille) and the augmentation suffix “-million”. The number of zeros in a number written in the American system can be found by the formula: 3x + 3, where x is a Latin ordinal
• English system most widespread in the world, it is used in Germany, Spain, Hungary, Poland, Czech Republic, Denmark, Sweden, Finland, Portugal. The names of numbers according to this system are built as follows: the suffix “-million” is added to the Latin numeral, the next number (1000 times larger) is the same Latin numeral, but the suffix “-billion” is added. The number of zeros in the number, which is written in the English system and ends with the suffix “-million”, can be found by the formula: 6x + 3, where x is a Latin ordinal number. The number of zeros in numbers ending with the suffix “-billion” can be found by the formula: 6x + 6, where x is a Latin ordinal number.

Only the word billion passed from the English system to the Russian language, which is nevertheless more correct to call it as the Americans call it - billion (since the American system of naming numbers is used in Russian).

In addition to numbers that are written in the American or English system using Latin prefixes, off-system numbers are known that have their own names without Latin prefixes.

Proper names of large numbers

• Vigintillion (from Lat.viginti - twenty) - 10 63
• Centillion (from Lat.centum - one hundred) - 10 303
• Million (from Latin mille - thousand) - 10 3003

For numbers over a thousand, the Romans did not have their own names (all the names of numbers were further compound).

Compound names for large numbers

In addition to proper names, for numbers greater than 10 33, compound names can be obtained by combining prefixes.

Compound names for large numbers

• 10 123 - quadragintillion
• 10 153 - quinquagintillion
• 10 183 - sexagintillion
• 10 213 - septuagintillion
• 10 243 - octogintillion
• 10 273 - nonagintillion
• 10,303 - centillion

Further names can be obtained by direct or reverse order of Latin numerals (as it is not known correctly):

• 10 306 - antcentillion or centunillion
• 10 309 - duocentillion or centduollion
• 10 312 - trecentillion or centtrillion
• 10 315 - quattorcentillion or centquadrillion
• 10 402 - tretrigintacentillion or centtretrigintillion

The second spelling is more consistent with the construction of numbers in Latin and avoids ambiguities (for example, in the number trecentillion, which, according to the first spelling, is 10 903 and 10 312).

• 10 603 - ducentillion
• 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 15003 - quinquemillion
• 10 308760 -ion
• 10 3000003 - Million
• 10 6000003 - duomiliamilillion

Myriad- 10 000. The name is outdated and practically not used. However, the word “myriads” is widely used, which does not mean a certain number, but an innumerable, uncountable set of something.

Googol ( English . googol) — 10 100. This number was first written by the American mathematician Edward Kasner in 1938 in the journal Scripta Mathematica in the article “New Names in Mathematics”. According to him, his 9-year-old nephew Milton Sirotta suggested the name so. This number became common knowledge thanks to the Google search engine named after him.

Asankheya(from Chinese asenci - uncountable) - 10 1 4 0. This number is found in the famous Buddhist treatise Jaina Sutra (100 BC). It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Googolplex ( English . Googolplex) — 10 ^ 10 ^ 100. This number was also invented by Edward Kasner and his nephew, it means one with a googol of zeros.

Skuse's number (Skewes' number, Sk 1) means e to the e to the e to the 79th power, that is, e ^ e ^ e ^ 79. This number was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) in the proof of the Riemann conjecture concerning prime numbers. Later, Riel (te Riele, HJJ "On the Sign of the Difference P (x) -Li (x)." Math. Comput. 48, 323-328, 1987) reduced the Skuse number to e ^ e ^ 27/4, which is approximately 8.185 10 ^ 370. However, this number is not an integer, so it is not included in the table of large numbers.

Skewes' second number (Sk2) is equal to 10 ^ 10 ^ 10 ^ 10 ^ 3, that is, 10 ^ 10 ^ 10 ^ 1000. This number was introduced by J. Skuse in the same article to denote the number up to which the Riemann hypothesis is valid.

For very large numbers, it is inconvenient to use powers, so there are several ways to write numbers - notation by Knuth, Conway, Steinhouse, etc.

Hugo Steinhouse proposed to write large numbers inside geometric shapes (triangle, square and circle).

The mathematician Leo Moser refined Steinhouse's notation by suggesting that after the squares, draw pentagons instead of circles, then hexagons, etc. Moser also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings.

Steinhouse came up with two new super-large numbers: Mega and Megiston. In Moser's notation, they are written as follows: Mega – 2, Megiston- 10. Leo Moser also proposed to call a polygon with the number of sides equal to mega - megagon, and also proposed the number “2 in Megagon” - 2. The last number is known as Moser's number or just like Moser.

There are numbers greater than Moser. The largest number used in mathematical proof is number Graham(Graham's number). It was first used in 1977 to prove one estimate in Ramsey's theory. This number is associated with bichromatic hypercubes and cannot be expressed without a special 64-level system of special mathematical symbols introduced by Knuth in 1976. Donald Knuth (who wrote The Art of Programming and created the TeX editor) came up with the concept of superdegree, which he proposed to write down with arrows pointing up:

In general

Graham suggested G-numbers:

The G 63 number is called the Graham number, often denoted simply G. This number is the largest known number in the world and is listed in the Guinness Book of Records.

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

What are the giant numbers?

Meanwhile, numbers denoting degrees 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 usually called a billion.

Many adults can accurately write numbers such as a million - 1,000,000 and a billion - 1,000,000,000. With a trillion it is already more difficult, but almost everyone will cope - 1,000,000,000,000. And then a territory unknown to many begins.

Getting to know the big numbers closer

Difficult, however, there is nothing, the main thing is to understand the system of 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.

The names can also be dealt with 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 visualize these numbers. 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 the idea that a trillion is something absolutely immense. But how much is a trillion more than a billion? How big is it?

For many more than a billion, the concept of "the mind is incomprehensible" begins. Indeed, a billion kilometers or a trillion is not a very big difference 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 that kind of money still cannot be earned in a lifetime. But let's count a little by connecting imagination.

The housing stock of Russia and four football fields as examples

For every person on earth, there is a land area of ​​100x200 meters. These are about four football fields. But if people are not 7 billion, but seven trillion, then everyone will get only a piece of land 4x5 meters. Four football fields against the front garden area 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 of 100 square meters. That is, about 3 billion square meters of private buildings. 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 total 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 we manage to get a sextillion of notebooks, then the entire planet, including the oceans, will be under a layer 100 meters thick.

Let's count to a decillion

Let's count some more. For example, a matchbox enlarged a thousand times would be the size of a sixteen-story building. An increase in a million times will give "boxes" that are larger in area than St. Petersburg. Enlarged a billion times, the box won't fit on our planet. On the contrary, the Earth will fit into 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 further increase. For ease of perception, we will 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 lined up in a row would extend beyond the star α Centauri by 9 trillion kilometers.

Another thousandfold magnification (sextillion) will allow matchboxes lined up to line our entire Milky Way galaxy in a lateral direction. A septillion matchbox would stretch 50 quintillion kilometers. Light can travel such a distance in 5 million 260 thousand years. And the boxes laid out in two rows would stretch as far as the Andromeda galaxy.

There are only three numbers left: octillion, nonillion and decillion. You have to strain your imagination. An octillion of boxes forms a continuous line of 50 sextillion kilometers. It is over five billion light years. Not every telescope mounted on one edge of such an object could 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, there 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 put together.

Decillion. The magnitude, or 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 a decillion times would contain the entire part of the Universe known to mankind 20 trillion times. It is impossible even to imagine something like that.

Small calculations showed how huge the numbers have been known to mankind for several centuries. In modern mathematics, numbers many times exceeding 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. Googol is greater than the total number of elementary particles in the visible part of the Universe. This makes googol an abstract number that has little practical use.

In the names of Arabic numbers, each digit belongs to its own category, and every three digits form a class. Thus, the last digit in a number denotes the number of ones in it and is called, respectively, the ones place. The next, second from the end, number denotes tens (tens place), and the third from the end number indicates the number of hundreds in the number - hundreds place. Further, the discharges in the same way are repeated in turn in each class, already denoting units, tens and hundreds in classes of thousands, millions, and so on. If the number is small and does not contain tens or hundreds, it is customary to take them as zero. Classes group numbers in numbers of three, often in calculating devices or records between classes, a period or a space is put in order to visually separate them. This is 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 are using the decimal system, the basic unit of measure for quantity is ten, or 10 1. Accordingly, with an increase in the number of digits in a number, the number of tens also increases 10 2, 10 3, 10 4, etc. Knowing the number of tens, you can easily determine the class and place of the number, for example, 10 16 is tens of quadrillion, and 3 × 10 16 is three tens of quadrillion. The decomposition of numbers into decimal components is as follows - each digit is displayed in a separate summand, multiplied by the required coefficient 10 n, where n is the position of the digit from left to right.
For instance: 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 used in writing decimal fractions: 10 (-1) is 0.1 or one tenth. Similarly with the previous paragraph, you can expand the decimal number, n in this case will denote the position of the digit from the comma from right to left, for example: 0.347629 = 3 × 10 (-1) + 4 × 10 (-2) + 7 × 10 (-3) + 6 × 10 (-4) + 2 × 10 (-5) + 9 × 10 (-6 )

Decimal names. Decimal numbers are read according to the last digit after the decimal point, for example 0.325 - three hundred twenty-five thousandths, where thousandths is the last digit of 5.

Table of names of large numbers, digits and classes