Back 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

Southern and Eastern Slavic peoples to write numbers, they used alphabetical numbering. 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. In this case, the numerical values ​​of the letters increased in the same order in which the letters in the Greek alphabet followed (the order of letters 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-16th centuries this word was supplanted by the word "forty", which originally meant a sack containing 40 squirrel or sable skins. There are two options for the origin of the word "thousand": from the old name "fat one hundred" or from a modification of the Latin word centum - "one hundred".

The name "million" first appeared in Italy in 1500 and was formed by adding a magnifying 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" of 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 of that time, slightly different from 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 augmentation 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	one hundred		hecto-	centi-	About half the number of all states on Earth
10 3	one 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 internal gross product 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 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 direct 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

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).

This is a tablet for studying numbers from 1 to 100. This manual is suitable for children over 4 years old.

Those familiar with Montessori training have probably seen such a sign before. She has many applications and now we will get to know them.

The child must know perfectly the numbers up to 10, before starting to work with the table, since counting up to 10 is the basis for learning numbers up to 100 and above.

Using this table, the child will learn the names of numbers up to 100; count up to 100; sequence of numbers. You can also practice counting in 2, 3, 5, etc.

The table can be copied here

It consists of two parts (two-sided). Copy on one side of the sheet a table with numbers up to 100, and on the other, empty cells where you can exercise. Laminate the table so that the child can write on it with markers and wipe it off easily.

How to use the table

	1. The table can be used to study numbers from 1 to 100. Starting at 1 and counting up to 100. Initially, the parent / teacher shows how to do this. It is important for the child to notice the principle by which numbers are repeated.
	2. On the laminated table, mark one number. The child should say the next 3-4 numbers.
	3. Mark some numbers. Ask your child for their names. The second version of the exercise - the parent calls arbitrary numbers, and the child finds and marks them.
	4. Counting in 5. The child counts 1,2,3,4,5 and marks the last (fifth) number.
	5. If you once again copy the template with numbers and cut it, you can make cards. They can be arranged in the table as you will see in the following lines. In this case, the table was copied on a blue cardboard, which would be easily distinguished from the white background of the table.
	6. Cards can be placed on the table and counted - call a number by placing its card. This helps the child learn all the numbers. In this way he will practice. Before that, it is important that the parent divides the cards by 10 (1 to 10; 11 to 20; 21 to 30, etc.). The child takes a card, puts it down and says a number.
	7. When the child has already advanced with the score, you can go to the empty table and place the cards there.
	8. Counting horizontally or vertically. Arrange the cards in a column or a row and read all the numbers in order, following the regularity of their change - 6, 16, 26, 36, etc.
	9. Write down the missing number. The parent writes arbitrary numbers to an empty table. The child must complete the empty cells.

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

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

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

But back to our native scale. Want to know what's coming after the trillion? Please:

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

At this number, our short scale does not hold up, and in the future, the mantisa increases progressively.

10 100 googol
10 123 quadragintillion
10,153 quinquagintillion
10 183 sexagintillion
10 213 septuagintillion
10,243 octogintillion
10,273 nonagintillion
10,303 centillion
10,306 centunillion
10,309 centduollion
10 312 cent trillion
10,315 cents quadrillion
10 402 centretrigintillion
10 603 ducentillion
10,903 trecentillion
10 1203 quadringentillion
10 1503 quingentillion
10 1803 sescentillion
10 2103 septingentillion
10 2403 oxtingentillion
10 2703 nongentillion
10 3003 million
10 6003 duomillion
10 9003 tremillion
10 3000003 Million
10 6000003 duomiliamilillion
10 10 100 googolplex
10 3 × n + 3 zillion

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

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

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

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

It is known that numbers are infinite and only a few have their own names, because most of the numbers received names consisting of small numbers. Largest numbers needs to be denoted 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 using numbers Latin, adding to them the inflection "-million", thus the bimillion became a billion, and a 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 that are 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, and 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 Schücke 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 hundreds of 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. The boy also suggested the name "googlex", a number with googol zeros.

But Claude Shannon in the middle of the twentieth century, evaluating moves in 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, that is how many cosmic cycles, according to Buddhists, are needed to find nirvana.

Stanley Skewes described large quantities as "Skewes' first 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, it becomes problematic 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, they are all different, at the heart of 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.

This is a tablet for studying numbers from 1 to 100. This manual is suitable for children over 4 years old.
Those familiar with Montessori training have probably seen such a sign before. She has many applications and now we will get to know them.
The child must know perfectly the numbers up to 10, before starting to work with the table, since counting up to 10 is the basis for learning numbers up to 100 and above.
Using this table, the child will learn the names of numbers up to 100; count up to 100; sequence of numbers. You can also practice counting in 2, 3, 5, etc.

The table can be copied here

It consists of two parts (two-sided). Copy on one side of the sheet a table with numbers up to 100, and on the other, empty cells where you can exercise. Laminate the table so that the child can write on it with markers and wipe it off easily.

How to use the table

1. The table can be used to study numbers from 1 to 100.
Starting at 1 and counting up to 100. Initially, the parent / teacher shows how to do this.
It is important for the child to notice the principle by which numbers are repeated.

2. On the laminated table, mark one number. The child should say the next 3-4 numbers.

3. Mark some numbers. Ask your child for their names.
The second version of the exercise - the parent calls arbitrary numbers, and the child finds and marks them.

4. Counting in 5.
The child counts 1,2,3,4,5 and marks the last (fifth) number.
Continues counting 1,2,3,4,5 and marks the last number until it reaches 100. Then it lists the marked numbers.
Similarly, he learns to count through 2, 3, etc.

5. If you once again copy the template with numbers and cut it, you can make cards. They can be arranged in the table as you will see in the following lines.
In this case, the table was copied on a blue cardboard, which would be easily distinguished from the white background of the table.

6. Cards can be placed on the table and counted - call a number by placing its card. This helps the child learn all the numbers. In this way he will practice.
Before that, it is important that the parent divides the cards by 10 (1 to 10; 11 to 20; 21 to 30, etc.). The child takes a card, puts it down and says a number.