The sum with 10 zeros is what they call it. Naming systems for large numbers

Even in the fourth grade I was interested in the question: "What are the names of numbers over a billion? 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, searches have accelerated significantly. Now I present all the information I have found so that others can also answer the question: "What are the names of large and very large numbers?"

A bit of history

The southern and eastern Slavic peoples used alphabetical numbering to write numbers. Moreover, among the Russians, not all letters played the role of numbers, but only those that are in the Greek alphabet. A special "titlo" icon was placed above the letter denoting the number. At the same time, the numerical values of the letters increased in the same order in which the letters in the Greek alphabet followed (the order of the letters in the Slavic alphabet was somewhat 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 the numbers. For example, until the 15th century, the number "twenty" was designated as "two ten" (two tens), but then it was shortened for a faster pronunciation. Until the 15th century the number "forty" was denoted by the word "fourty", and in the 15th and 16th centuries this word was supplanted by the word "forty", which originally meant a sack containing 40 squirrel or sable skins. There are two variants of the origin of the word "thousand": from the old name "thick one hundred" or from the modification of the Latin word centum - "one hundred".

The name "million" first appeared in Italy in 1500 and was formed by adding an augmenting suffix to the number "millet" - a thousand (that is, it meant "a large thousand"), it penetrated into the Russian language later, and before that the same meaning in in Russian it was denoted 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 augmentation 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 of the wealthy had $ 1,000,000,000. 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" names are given large numbers 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".

Naming Principles and List of Large Numbers

All the names of large numbers are constructed in a rather simple way: 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 thousand (mille) and the augmenting suffix-million. There are two main types of names for large numbers in the world:
3x + 3 system (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 the 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 a billion, which is also called a billion).

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

Number	Name	Latin numeral	Increasing prefix SI	Reducing prefix SI	Practical value
10 1	ten		deca	deci-	Number of fingers on 2 hands
10 2	hundred		hecto-	centi-	About half the number of all states on Earth
10 3	thousand		kilo	Milli-	Approximate number of days in 3 years
10 6	million	unus (I)	mega-	micro-	5 times the number of drops in a 10 liter bucket of water
10 9	billion (billion)	duo (II)	giga-	nano-	Approximate population of India
10 12	trillion	tres (III)	tera-	pico	1/13 of the gross domestic product of Russia in rubles for 2003
10 15	quadrillion	quattor (IV)	peta-	femto-	1/30 parsec length in meters
10 18	quintillion	quinque (V)	ex-	atto-	1/18 of the number of grains from the legendary chess inventor award
10 21	sextillion	sex (VI)	zetta-	chain	1/6 the mass of the planet Earth in tons
10 24	septillion	septem (VII)	yotta-	yokto-	The number of molecules in 37.2 liters of air
10 27	octillion	octo (VIII)	no-	sieve-	Half the mass of Jupiter in kilograms
10 30	quintillion	novem (IX)	de-	thread-	1/5 of all microorganisms on the planet
10 33	decillion	decem (X)	una-	roaring	Half the mass of the Sun in grams

Number	Name	Latin numeral	Practical value
10 36	andecillion	undecim (XI)
10 39	duodecillion	duodecim (XII)
10 42	tredecillion	tredecim (XIII)	1/100 of the number of air molecules on Earth
10 45	quattordecillion	quattuordecim (XIV)
10 48	quindecillion	quindecim (XV)
10 51	sexdecillion	sedecim (XVI)
10 54	septemdecillion	septendecim (XVII)
10 57	octodecillion		So many elementary particles in the sun
10 60	novemdecillion
10 63	vigintillion	viginti (XX)
10 66	anvigintillion	unus et viginti (XXI)
10 69	duovigintillion	duo et viginti (XXII)
10 72	trevigintillion	tres et viginti (XXIII)
10 75	quattorvigintillion
10 78	quinvigintillion
10 81	sexvigintillion		So many elementary particles in the universe
10 84	septemwigintillion
10 87	octovigintillion
10 90	novemvigintillion
10 93	trigintillion	triginta (XXX)
10 96	antrigintillion

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 - quinquaginta, L
10,183 - 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 by direct or reverse order of Latin numerals (as it is correct, it is not known):

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

I believe that the second spelling option will be the most correct, since it is more consistent with the construction of numerals in Latin and avoids ambiguities (for example, in the number trecentillion, which, according to the first spelling, is 10 903 and 10 312).

A bit of history

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.

The name "million" first appeared in Italy in 1500 and was formed by adding a magnifying suffix to the number "millet" - a thousand (meaning "a large thousand"), it penetrated into the Russian language later, and before that the same meaning in in Russian it was denoted 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 augmentation 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 of the wealthy had $ 1,000,000,000. 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".

Naming Principles and List of Large Numbers
All the names of large numbers are constructed in a rather simple way: 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 (mille) and the augmenting suffix-million. There are two main types of names for large numbers in the world:
3x + 3 system (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 the Latin ordinal number) - this system is the 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 a billion, which is also called a billion).

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

Number	Name	Latin numeral	Increasing prefix SI	Reducing prefix SI	Practical value
10 1	ten		deca	deci-	Number of fingers on 2 hands
10 2	hundred		hecto-	centi-	About half the number of all states on Earth
10 3	thousand		kilo	Milli-	Approximate number of days in 3 years
10 6	million	unus (I)	mega-	micro-	5 times the number of drops in a 10 liter bucket of water
10 9	billion (billion)	duo (II)	giga-	nano-	Approximate population of India
10 12	trillion	tres (III)	tera-	pico	1/13 of the gross domestic product of Russia in rubles for 2003
10 15	quadrillion	quattor (IV)	peta-	femto-	1/30 parsec length in meters
10 18	quintillion	quinque (V)	ex-	atto-	1/18 of the number of grains from the legendary chess inventor award
10 21	sextillion	sex (VI)	zetta-	chain	1/6 the mass of the planet Earth in tons
10 24	septillion	septem (VII)	yotta-	yokto-	The number of molecules in 37.2 liters of air
10 27	octillion	octo (VIII)	no-	sieve-	Half the mass of Jupiter in kilograms
10 30	quintillion	novem (IX)	de-	thread-	1/5 of all microorganisms on the planet
10 33	decillion	decem (X)	una-	roaring	Half the mass of the Sun in grams

The pronunciation of the numbers below is often different.

Number	Name	Latin numeral	Practical value
10 36	andecillion	undecim (XI)
10 39	duodecillion	duodecim (XII)
10 42	tredecillion	tredecim (XIII)	1/100 of the number of air molecules on Earth
10 45	quattordecillion	quattuordecim (XIV)
10 48	quindecillion	quindecim (XV)
10 51	sexdecillion	sedecim (XVI)
10 54	septemdecillion	septendecim (XVII)
10 57	octodecillion		So many elementary particles in the sun
10 60	novemdecillion
10 63	vigintillion	viginti (XX)
10 66	anvigintillion	unus et viginti (XXI)
10 69	duovigintillion	duo et viginti (XXII)
10 72	trevigintillion	tres et viginti (XXIII)
10 75	quattorvigintillion
10 78	quinvigintillion
10 81	sexvigintillion		So many elementary particles in the universe
10 84	septemwigintillion
10 87	octovigintillion
10 90	novemvigintillion
10 93	trigintillion	triginta (XXX)
10 96	antrigintillion

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 - quinquaginta, L

10,183 - 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 by direct or reverse order of Latin numerals (as it is correct, it is not known):

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

Perelman Ya.I. "Entertaining arithmetic". - M .: Triada-Litera, 1994, pp. 134-140

Vygodsky M. Ya. "Handbook of Elementary Mathematics". - S-Pb., 1994, pp. 64-65

"Encyclopedia of Knowledge". - comp. IN AND. Korotkevich. - St. Petersburg: Owl, 2006, p. 257

"Interesting about physics and mathematics." - Library Kvant. no. 50. - M .: Nauka, 1988, p. 50

It is known that numbers endless set and only a few have their own names, because most of the numbers received names consisting of small numbers. The largest numbers need to be labeled in some way.

"Short" and "long" scale

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

This system was described in his monograph by a Frenchman Nicolas Schuquet, he recommended the use of Latin numerals, adding to them the inflection "-million", so the bimillion became a billion, and trillion - a trillion, and so on.

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

So 109 got the name 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, in the United States, its own order of naming large numbers was created. According to him, the construction of names is carried out in the same way, but only the numbers differ.

The previous system continued to be applied in the UK, therefore 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.

Short scale found active use in the USA, Canada, Great Britain, Greece, Romania, 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 greater than a decillion, scientists decided to combine several Latin prefixes, so the undecillion, quattordecillion and others were named. If you use the Schuecke system, then, according to her, gigantic numbers will acquire the names "Vigintillion", "Centillion" and "Million" (103003), respectively, according to the long scale, such a number will receive the name "Millionbillion" (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.

V Ancient Rus its own number system has long been used. Hundreds of thousands were denoted by the word legion, a million were called leodrome, tens of millions were crows, hundreds of millions were called a deck. It was "small count", but "great count" used the same words, but the meaning was different, for example, leodr could mean a legion of legions (1024), and the deck was already ten ravens (1096).

It happened that the names of the numbers were invented by children, so the mathematician Edward Kasner gave the idea young Milton Sirotta, who suggested giving a name to a number with a hundred zeros (10100) just Googol... This number received the greatest publicity in the nineties of the twentieth century, when the search engine Google was named in his honor. Also, the boy suggested the name "googlex", a number with googol zeros.

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

In the ancient work of Buddhists Jaina Sutras, written almost twenty two centuries ago, the number "asankheya" (10140) is noted, this is how many cosmic cycles, according to Buddhists, are needed to find nirvana.

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

Notations

Of course, depending on the number of degrees contained in the number, there is a problem in fixing it in writing, and reading, error bases. some numbers can't fit on multiple pages, so mathematicians have come up with notations for capturing large numbers.

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

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

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 with nine zeros (1,000,000,000) - what is the name of the number?

A short list of numbers and their quantitative designation

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

Grouping zeros

1,000,000,000 - what is the name of a number that has 9 zeros? This is a billion. For convenience, it is customary to group large numbers into three sets, separated from each other by a space or punctuation marks such as a comma or period.

This is done to make it easier to read and understand the quantitative value. For example, what is the name of the number 1,000,000,000? In this form, it is worthwhile to pretend a little, to count. And if you write 1,000,000,000, then immediately the task is visually easier, so you need to count not zeros, but triples of zeros.

Numbers with very many zeros

The most popular are Million and Billion (1,000,000,000). What is the name of a number with 100 zeros? This is the googol figure, also called Milton Sirotta. This is a wildly huge amount. Do you think this number is large? Then how 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 an infinite universe.

Is 1 billion a lot?

There are two scales of measurement - short and long. Worldwide in the field of 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 that is used in some European countries, including in France, and was previously used in Great Britain (until 1971), where a billion was 1 million million, that is, one and 12 zeros. This gradation is also called the long-term scale. The short scale is now dominant in financial and scientific matters.

Some European languages such as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German use a billion (or a billion) names 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 was called “lemon”.

The word “billion” is now used internationally. it natural number, which is displayed in decimal as 10 9 (one and 9 zeros). There is also another name - billion, which is not used in Russia and the CIS countries.

Billion = Billion?

Such a word as billion is used to designate a billion only in those states in which the "short scale" is taken as the basis. These are countries like Russian Federation, United Kingdom of Great Britain and Northern Ireland, USA, Canada, Greece and Turkey. In other countries, the term billion means the number 10 12, that is, one and 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, the billion had 12 zeros. However, everything changed after the appearance of the main textbook on arithmetic (by Tranchan) in 1558), where a billion is already a number with 9 zeros (one thousand million).

For the next several centuries, these two concepts were used on an equal basis with each other. In the middle of the 20th century, namely in 1948, France switched to a long-scale number 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 has used a long-term billion, but since 1974, UK official statistics have used a 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 persisted.

V 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:

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

However, there is nothing difficult, 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." Next 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 such 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 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 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 with an area 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 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 short, there will not be a trillion bricks in all of Russia.

One quadrillion of 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 screen our entire Milky Way galaxy laterally. A septillion matchbox 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 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 non-million 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 by a decillion, 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.