17 digit number name. What is the name of the largest number in the world?

Back in the fourth grade, I was interested in the question: “What are numbers greater than a billion called? And why?” Since then, I have been looking for all the information on this issue for a long time and collecting it bit by bit. But with the advent of Internet access, searching has accelerated significantly. Now I present all the information I found so that others can answer the question: “What are large and very large numbers called?”

A little history

Southern and eastern Slavic peoples Alphabetical numbering was used to record numbers. Moreover, for the Russians, not all letters played the role of numbers, but only those that are in the Greek alphabet. A special “title” icon was placed above the letter indicating the number. At the same time, the numerical values ​​of the letters increased in the same order as the letters in the Greek alphabet (the order of the letters of the Slavic alphabet was slightly different).

In Russia, Slavic numbering was preserved until the end of the 17th century. Under Peter I, the so-called “Arabic numbering” prevailed, which we still use today.

There were also changes in the names of numbers. For example, until the 15th century, the number "twenty" was written as "two tens" (two tens), but was then shortened for faster pronunciation. Until the 15th century, the number "forty" was denoted by the word "fourty", and in the 15th-16th centuries this word was replaced by the word "forty", which originally meant a bag in which 40 squirrel or sable skins were placed. There are two options about the origin of the word “thousand”: from the old name “thick hundred” or from a modification of the Latin word centum - “hundred”.

The name “million” first appeared in Italy in 1500 and was formed by adding an augmentative suffix to the number “mille” - a thousand (i.e., it meant “big thousand”), it penetrated into the Russian language later, and before that the same meaning in in Russian it was designated by the number "leodr". The word “billion” came into use only since the Franco-Prussian War (1871), when the French had to pay Germany an indemnity of 5,000,000,000 francs. Like "million," the word "billion" comes from the root "thousand" with the addition of an Italian magnifying suffix. In Germany and America for some time the word “billion” meant the number 100,000,000; This explains that the word billionaire was used in America before any rich person had $1,000,000,000. In the ancient (18th century) “Arithmetic” of Magnitsky, a table of the names of numbers is given, brought to the “quadrillion” (10^24, according to the system through 6 digits). Perelman Ya.I. in the book "Entertaining Arithmetic" the names are given large numbers of that time, slightly different from today: septillion (10^42), octalion (10^48), nonalion (10^54), decalion (10^60), endecalion (10^66), dodecalion (10^72) and It is written that “there are no further names.”

Principles for constructing names and a list of large numbers

All names of large numbers are constructed quite in a simple way: the Latin ordinal number comes at the beginning, and the suffix -million is added to it at the end. An exception is the name "million" which is the name of the number thousand (mille) and the augmentative suffix -million. There are two main types of names for large numbers in the world:
system 3x+3 (where x is a Latin ordinal number) - this system is used in Russia, France, USA, Canada, Italy, Turkey, Brazil, Greece
and the 6x system (where x is a Latin ordinal number) - 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 suffix -billion (from it we borrowed billion, which is also called billion).

Below is a general list of numbers used in Russia:

...
• 10,100 - googol (the number was invented by the 9-year-old nephew of the American mathematician Edward Kasner)
• 10 123 - quadragintillion (quadraginta, XL)
• 10 153 - quinquagintillion (quinquaginta, L)
• 10 183 - sexagintillion (sexaginta, LX)
• 10,213 - septuagintillion (septuaginta, LXX)
• 10,243 - octogintillion (octoginta, LXXX)
• 10,273 - nonagintillion (nonaginta, XC)
• 10 303 - centillion (Centum, C)

Further names can be obtained either directly or in reverse order Latin numerals (which is correct is not known):

• 10 306 - ancentillion or centunillion
• 10 309 - duocentillion or centullion
• 10 312 - trecentillion or centtrillion
• 10 315 - quattorcentillion or centquadrillion
• 10 402 - tretrigyntacentillion or centretrigyntillion

I believe that the second spelling would be the most correct, since it is more consistent with the construction of numerals in the Latin language and allows us to avoid ambiguities (for example, in the number trcentillion, which, according to the first spelling, is also 10 903 and 10,312).

Many people are interested in questions about what large numbers are called and what number is the largest in the world. With these interesting questions and we will look into this in this article.

Story

The southern and eastern Slavic peoples used alphabetical numbering to record numbers, and only those letters that are in the Greek alphabet. A special “title” icon was placed above the letter that designated the number. The numerical values ​​of the letters increased in the same order as the letters 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 also changed. Thus, until the 15th century, the number “twenty” was designated as “two tens” (two tens), and then it was shortened for faster pronunciation. The number 40 was called “fourty” until the 15th century, then it was replaced by the word “forty,” which originally meant a bag containing 40 squirrel or sable skins. The name “million” appeared in Italy in 1500. It was formed by adding an augmentative suffix to the number “mille” (thousand). Later this name came to the Russian language.

In the ancient (18th century) “Arithmetic” of Magnitsky, a table of the names of numbers is given, brought to the “quadrillion” (10^24, according to the system through 6 digits). Perelman Ya.I. the book “Entertaining Arithmetic” gives the names of large numbers of that time, slightly different from today: septillion (10^42), octalion (10^48), nonalion (10^54), decalion (10^60), endecalion (10^ 66), dodecalion (10^72) and it is written that “there are no further names.”

Ways to construct names for large numbers

There are 2 main ways to name large numbers:

• American system, which is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are constructed quite simply: the Latin ordinal number comes first, and the suffix “-million” is added to it at the end. An exception is the number “million”, which is the name of the number thousand (mille) and the augmentative suffix “-million”. The number of zeros in a number, which is written according to the American system, can be found out by the formula: 3x+3, where x is the Latin ordinal number
• English system most common 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 constructed 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 according to English system and ends with the suffix “-million”, can be recognized by the formula: 6x+3, where x is the Latin ordinal number. The number of zeros in numbers ending with the suffix “-billion” can be found using the formula: 6x+6, where x is the Latin ordinal number.

Only the word billion passed from the English system into the Russian language, which is still more correctly called as the Americans call it - billion (since in Russian it is used American system names of numbers).

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

Proper names for large numbers

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

For numbers greater than a thousand, the Romans did not have their own names (all names for numbers were then composite).

Compound names of large numbers

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

Compound names of 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 (which is correct is not known):

• 10 306 - ancentillion or centunillion
• 10 309 - duocentillion or centullion
• 10 312 - trcentillion or centtrillion
• 10 315 - quattorcentillion or centquadrillion
• 10 402 - tretrigyntacentillion or centretrigintillion

The second spelling is more consistent with the construction of numerals in the Latin language and allows us to avoid ambiguities (for example, in the number trecentillion, which according to the first spelling is both 10,903 and 10,312).

• 10 603 - decentillion
• 10,903 - trcentillion
• 10 1203 - quadringentillion
• 10 1503 — quingentillion
• 10 1803 - sescentillion
• 10 2103 - septingentillion
• 10 2403 — octingentillion
• 10 2703 — nongentillion
• 10 3003 - million
• 10 6003 - duo-million
• 10 9003 - three million
• 10 15003 — quinquemillillion
• 10 308760 -ion
• 10 3000003 — mimiliaillion
• 10 6000003 — duomimiliaillion

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

Googol ( English . googol) — 10 100. The American mathematician Edward Kasner first wrote about this number 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 calling the number this way. This number became well known thanks to the Google search engine named after him.

Asankheya(from Chinese asentsi - 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 achieve nirvana.

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

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

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

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

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

Mathematician Leo Moser refined Steinhouse's notation, proposing to draw pentagons, then hexagons, etc. after squares rather than circles. Moser also proposed a formal notation for these polygons so that the numbers could be written without drawing complex pictures.

Steinhouse came up with two new super-large numbers: Mega and Megiston. In Moser 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 suggested the number “2 in Megagon” - 2. Last number known as Moser's number or just like Moser.

There are numbers larger than Moser. The largest number that has been used in a mathematical proof is number Graham(Graham's number). It was first used in 1977 to prove an estimate in Ramsey 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 superpower, which he proposed to write with arrows pointing up:

In general

Graham proposed G-numbers:

The number G 63 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.

It is known that an infinite number of numbers and only a few have their own names, because most numbers received names consisting of small numbers. The largest numbers need to be designated somehow.

"Short" and "long" scale

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

This system was described in his monograph by the Frenchman Nicolas Chuquet, he recommended using numerals Latin language, adding the inflection “-million” to them, so bimillion became billion, and three million became trillion, and so on.

But according to the proposed system, he called the numbers between a million and a billion “a thousand millions.” It was not comfortable to work with such a gradation and in 1549 by the Frenchman Jacques Peletier advised to name the numbers located in the indicated interval, again using Latin prefixes, while introducing a different ending - “-billion”.

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

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

The previous system continued to be used in Great Britain, which is why it was called British, although it was originally created by the French. But already in 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 used, 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 denote numbers larger than a decillion, scientists decided to combine several Latin prefixes, so undecillion, quattordecillion and others were named. If you use Schuke system, then, according to it, giant numbers will receive the names “vigintillion”, “centillion” and “million” (103003), respectively, according to the long scale, such a number will receive the name “billion” (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, and numbers over a million.

IN Ancient Rus' its own numerical system has been used for a long time. Hundreds of thousands were designated by the word legion, a million were called leodromes, tens of millions were ravens, hundreds of millions were called a deck. This was the “small count,” but the “great count” used the same words, only they had a different meaning, for example, leodr could mean a legion of legions (1024), and a deck could mean ten ravens (1096).

It happened that children came up with names for numbers, so the mathematician Edward Kasner gave the idea young Milton Sirotta, who proposed to name the number with a hundred zeros (10100) simply "googol". This number received the greatest publicity in the nineties of the twentieth century, when the Google search engine was named in its honor. The boy also suggested the name “googloplex,” a number with a googol of zeros.

But Claude Shannon in the middle of the twentieth century, assessing the moves in chess game, calculated that there are 10118 of them, now this "Shannon number".

In the ancient work of Buddhists "Jaina Sutras", written almost twenty-two centuries ago, notes the number “asankheya” (10140), which is exactly how many cosmic cycles, according to Buddhists, are necessary to achieve nirvana.

Stanley Skuse described large quantities as "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 record it in writing, and even in reading, error databases. Some numbers cannot be contained on several 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 Steinhaus and Knuth notations.

However, most large number- “Graham number”, used Ronald Graham in 1977 when performing mathematical calculations, and this is the number G64.

IN Everyday life Most people operate with fairly small numbers. Tens, hundreds, thousands, very rarely - millions, almost never - billions. A person’s usual idea of ​​quantity or magnitude is limited to approximately these numbers. Almost everyone has heard about trillions, but few have ever used them in any calculations.

What are they, giant numbers?

Meanwhile, numbers denoting 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:

Thousand;
Million;
Billion;
Trillion;
Quadrillion;
Quintillion;
Sextillion;
Septillion;
Octillion;
Quintillion;
Decillion.

In this system, each subsequent number is obtained by multiplying the previous one by a thousand. Billion is usually called billion.

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

Let's take a closer look at the big numbers

However, there is nothing complicated, the main thing is to understand the system of formation of large numbers and the principle of naming. As already mentioned, each subsequent number is a thousand times greater than the previous one. 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 figure out 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 Latin words“bi” (two), “three” (three), “quad” (four), etc.

Now let's try to visualize these numbers clearly. 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 more is a trillion than a billion? How big is it?

For many, beyond a billion the concept of “incomprehensible to the mind” 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 your entire life. But let's do a little math using our imagination.

Russia's housing stock and four football fields as examples

For every person on earth there is a land area measuring 100x200 meters. This is approximately four football fields. But if there are not 7 billion people, but seven trillion, then everyone will only get a piece of land 4x5 meters. Four football fields versus 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 buildings, you will get approximately 2.5 million houses, that is, 100 million two- and 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 are not 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 landmass with a layer 40 centimeters thick. If we manage to get a sextillion 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 magnified a thousand times would be the size of a sixteen-story building. An increase of a million times will give a “box” that is larger in area than St. Petersburg. Enlarged a billion times, the boxes would not fit on our planet. On the contrary, the Earth will fit into such a “box” 25 times!

Increasing the box gives an increase in its volume. It will be almost impossible to imagine such volumes with 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 boxes laid out in one row would stretch beyond the star α Centauri by 9 trillion kilometers.

Another thousandfold magnification (sextillion) would allow matchboxes lined up to span the entire length of our Milky Way galaxy. Septillion matchboxes would stretch over 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 to the Andromeda galaxy.

There are only three numbers left: octillion, nonillion and decillion. You'll have to use your imagination. An octillion boxes form a continuous line of 50 sextillion kilometers. This is more than five billion light years. Not every telescope installed on one edge of such an object could see its opposite edge.

Shall we count further? A nonillion matchboxes would fill the entire space of the known part of the Universe with an average density of 6 pieces per cubic meter. By earthly standards, it doesn’t seem like a lot - 36 matchboxes in the back of a standard Gazelle. But a nonillion matchboxes would have a mass billions of times greater than the mass of all the material objects in the known Universe combined.

Decillion. The size, or rather even the majesty, of this giant from the world of numbers is difficult to imagine. Just one example - six decillion boxes would no longer fit in the entire part of the Universe accessible to humanity for observation.

The majesty of this number is even more striking if you do not multiply the number of boxes, but increase the object itself. A matchbox, magnified a decillion times, would contain the entire part of the Universe known to mankind 20 trillion times. It’s impossible to even imagine this.

Small calculations showed how huge the numbers are, known to mankind for several centuries. 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 googol an abstract number that has little practical use.

Have you ever thought how many zeros there are in one million? This is a pretty simple question. What about a billion or a trillion? One followed by nine zeros (1000000000) - what is the name of the number?

A short list of numbers and their quantitative designation

• Ten (1 zero).
• One hundred (2 zeros).
• One thousand (3 zeros).
• Ten thousand (4 zeros).
• One hundred thousand (5 zeros).
• Million (6 zeros).
• Billion (9 zeros).
• Trillion (12 zeros).
• Quadrillion (15 zeros).
• Quintilion (18 zeros).
• Sextillion (21 zeros).
• Septillion (24 zeros).
• Octalion (27 zeros).
• Nonalion (30 zeros).
• Decalion (33 zeros).

Grouping of zeros

1000000000 - what is the name of a number that has 9 zeros? This is a billion. For convenience, large numbers are usually grouped into sets of three, separated from each other by a space or punctuation marks such as a comma or period.

This is done to make the quantitative value easier to read and understand. For example, what is the name of the number 1000000000? In this form, it’s worth straining a little and doing the math. And if you write 1,000,000,000, then the task immediately becomes visually easier, since you need to count not zeros, but triples of zeros.

Numbers with a lot of zeros

The most popular are million and billion (1000000000). What is the name of a number that has 100 zeros? This is a Googol number, so called by Milton Sirotta. This is a wildly huge amount. Do you think this number is large? Then what about a googolplex, a one followed by a googol of zeros? This figure is so large that it is difficult to come up with a meaning for it. In fact, there is no need for such giants, except to count the number of atoms in the infinite Universe.

Is 1 billion a lot?

There are two measurement scales - short and long. Around the world in science and finance, 1 billion is 1,000 million. This is on a short scale. According to it, this is a number with 9 zeros.

There is also a long scale which is used in some European countries, including in France, and was previously used in the UK (until 1971), where a billion was 1 million millions, that is, one followed by 12 zeros. This gradation is also called the long-term scale. The short scale is now predominant in financial and scientific matters.

Some European languages, such as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German, use billion (or billion) in this system. In Russian, a number with 9 zeros is also described for the short scale of a thousand million, and a trillion is a million million. This avoids unnecessary confusion.

Conversational options

In Russian colloquial speech after the events of 1917 - the Great October Revolution - and the period of hyperinflation in the early 1920s. 1 billion rubles was called “limard”. And in the dashing 1990s, a new slang expression “watermelon” appeared for a billion; a million were called “lemon.”

The word "billion" is now used in international level. This natural number, which is depicted in decimal system, like 10 9 (one and 9 zeros). There is also another name - billion, which is not used in Russia and the CIS countries.

Billion = billion?

A word such as billion is used to designate a billion only in those states in which the “short scale” is adopted as a basis. These are countries like Russian Federation, United Kingdom of Great Britain and Northern Ireland, USA, Canada, Greece and Türkiye. In other countries, the concept of a billion means the number 10 12, that is, one followed by 12 zeros. In countries with a “short scale”, including Russia, this figure corresponds to 1 trillion.

Such confusion appeared in France at a time when the formation of such a science as algebra was taking place. Initially, a billion had 12 zeros. However, everything changed after the appearance of the main manual on arithmetic (author Tranchan) in 1558), where a billion is already a number with 9 zeros (a thousand millions).

For several subsequent centuries, these two concepts were used on an equal basis with each other. In the mid-20th century, namely in 1948, France switched to a long scale numerical naming system. In this regard, the short scale, once borrowed from the French, is still different from the one they use today.

Historically, the United Kingdom used the long-term billion, but since 1974 official UK statistics have used the short-term scale. Since the 1950s, the short-term scale has been increasingly used in the fields of technical writing and journalism, although the long-term scale still persists.