What are the numbers after a million. The largest number in the world

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 example: 253 981 = 2 × 10 6 + 5 × 10 5 + 3 × 10 4 + 9 × 10 3 + 8 × 10 2 + 1 × 10 1

Also, the power of 10 is 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 read by the last digit after the decimal point, for example 0.325 - three hundred twenty-five thousandths, where thousandths are the last digit 5.

Table of names of large numbers, digits and classes

Have you ever wondered how many zeros there are in one million? This is a pretty straightforward 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 the task is immediately 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 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 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?

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 the long-term billion, but since 1974 the UK's 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.

Countless different numbers surrounds 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. Which of them is more, it is rather difficult to say, 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 about such a number, then 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 made it to the pages famous Book records.

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

History

Southern and Eastern Slavic peoples to write numbers, they used alphabetical numbering, 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 directly or reverse order Latin numerals (as 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

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 both 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 suggested recording 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 most a large number which was 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.

Naming systems for large numbers

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

In the American system, 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 "illion" is added to it. An exception is the name "million", which is the name of the number one thousand (lat. Mille) and the augmentation suffix "illion". This is how the numbers are obtained - trillion, quadrillion, quintillion, sextillion, etc. The American system is used in the USA, Canada, France and Russia. The number of zeros in a number written in the American system is determined by the formula 3 x + 3 (where x is a Latin numeral).

The European (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 constructed as follows: the suffix "illion" is added to the Latin numeral, the name of the next number (1000 times larger) is formed from the same Latin numeral, but with the suffix "illiard". That is, after a trillion in this system there is a trillion, and only then a quadrillion, followed by a quadrillion, etc. The number of zeros in a number written in the European system and ending with the suffix "illion" is determined by the formula 6 x + 3 (where x - Latin numeral) and by the formula 6 · x + 6 for numbers ending in "illiard". In some countries that use the American system, for example, Russia, Turkey, Italy, the word “billion” is used instead of the word “billion”.

Both systems come from France. French physicist and mathematician Nicolas Chuquet coined the words “byllion” and “trillion” (tryllion) and used them to denote the numbers 10 12 and 10 18, respectively, which served as the basis for the European system.

But some French mathematicians in the 17th century used the words "billion" and "trillion" for the numbers 10 9 and 10 12, respectively. This naming system became entrenched in France and America, and became known as American, while the original Choquet system continued to be used in Great Britain and Germany. France in 1948 returned to the Choquet system (i.e. European).

V last years the American system is replacing the European one, partly in Great Britain and so far hardly noticeable in other European countries. This is mainly due to the American insistence in financial transactions that $ 1,000,000,000 should be called a billion dollars. In 1974, the government of Prime Minister Harold Wilson announced that in official UK reports and statistics, the word billion would stand for 10 9, not 10 12.

12 - Dozen(from the French douzaine or Italian dozzina, which in turn originated from the Latin duodecim.)
A measure of the piece count of homogeneous objects. It was widely used before the introduction of the metric system. For example, a dozen handkerchiefs, a dozen forks. 12 dozen make up the gross. For the first time in the Russian language, the word "dozen" has been mentioned since 1720. It was originally used by sailors.

13 - Baker's dozen

The number is considered unlucky. Many western hotels do not have 13 rooms, but office buildings have 13 floors. There are no seats with this number in Italian opera houses. On almost all ships, after the 12th cabin, there is the 14th one.

144 - Gross- "big dozen" (from German Gro? - big)

A score equal to 12 dozen. It was usually used when counting small haberdashery and office supplies - pencils, buttons, writing pens, etc. A dozen gross is a mass.

1728 - Weight

Mass (obsolete) is a counting measure equal to a dozen gross, i.e. 144 * 12 = 1728 pieces. It was widely used before the introduction of the metric system.

666 or 616 - The number of the beast

A special number mentioned in the Bible (Book of Revelation 13:18, 14: 2). It is assumed that in connection with the assignment of a numerical value to the letters of the ancient alphabets, this number can mean any name or concept, the sum of the numerical values ​​of the letters of which is 666. These words can be: "Lateynos" (means in Greek everything Latin; suggested by Jerome ), "Nero Caesar", "Bonaparte" and even "Martin Luther". Some manuscripts read the number of the beast as 616.

Myriad - the word is outdated and practically not used, but the word "myriad" - (astronomer.) Is widely used, which means an innumerable, uncountable set of something.

Myriad was the largest number for which the ancient Greeks had a name. However, in the work "Psammit" ("The calculus of grains of sand") Archimedes showed how one can systematically construct and name arbitrarily large numbers. Archimedes called all the numbers from 1 to myriad (10,000) the first numbers, he called the myriad of myriads (10 8) the unit of the numbers of the second (dimyriad), the myriad of the myriad of second numbers (10 16) he called the unit of the third numbers (trimyriad), etc. ...

10 000 - darkness
100 000 - legion
1 000 000 - leodr
10 000 000 - raven or liar
100 000 000 - deck

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 24, then it was said - ten leodr, one hundred leodr, ..., and, finally, one hundred thousand leodr legion - 10 47; leodr leodrov -10 48 was called a raven and, finally, a deck of -10 49.

10 140 - Asankhei I (from Chinese asenci - incalculable)

Mentioned in the famous Jaina Sutra Buddhist treatise dating back to 100 BC. It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Googol(from the English. googol) - 10 100 , that is, one followed by 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" - this is trademark , a googol - number.

Googolplex(eng.googolplex) 10 10 100 - 10 to the power of googol.

The number also invented by Kasner and his nephew and means one with a googol of zeros, that is, 10 to the googol power. 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.

Skuse's number(Skewes` number) - Sk 1 e e e 79 - means e to the power of e to the power of e to the power of 79.

It was proposed by J. 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 ee 27/4, which is approximately equal 8.185 10 370.

It was introduced by J. Skuse in the same article to denote a number up to which the Riemann hypothesis is not valid. Sk 2 is equal to 10 10 10 10 3.

As you can imagine, the more degrees there are, the more difficult it is to understand which of the numbers is larger. 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.

Hugo Stenhouse notation(H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983) is pretty straightforward. Steinhaus (German Steihaus) proposed to write large numbers inside geometric shapes - a triangle, a square and a circle.

Steinhaus came up with super-large numbers and named the number 2 in a circle - Mega, 3 in a circle - Mezzon, and the number 10 in a circle is Megiston.

Mathematician Leo Moser modified 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 it was necessary to draw many circles 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:

• "n triangle" = nn = n.
• "n squared" = n = "n in n triangles" = nn.
• "n in pentagon" = n = "n in n squares" = nn.
• n = "n in n k-gons" = n [k] n.

In Moser's notation, the Steinhouse mega is written as 2, and the megiston as 10. Leo Moser suggested calling a polygon with the number of sides equal to mega - megagon... He also suggested the number "2 in Megagon", that is 2. This number became known as Moser number(Moser`s number) or just like a moser. But the Moser number is not the largest number either.

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