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Names of large numbers

Названия больших чисел

Back in the fourth grade I was interested in the question: "And how are the numbers called more than a billion, and why?".

Since then, I have been searching for all the information on this issue for a long time and collecting it according to crumbs. But with the advent of Internet access, the search has significantly accelerated.

Now I represent all the information I found, so that others could answer the question: "How are large and very large numbers called?".

History

The southern and eastern Slavic peoples used alphabetic numbering to write numbers. And for Russians the role of numbers was played not by all the letters, but only by those that are found in the Greek alphabet. Above the letter denoting the figure, a special "titlo" badge was placed. At the same time, the numerical values ​​of the letters increased in the same order as the letters in the Greek alphabet followed (the order of the letters of the Slavic alphabet was somewhat different).

In Russia, the 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.

In the names of numbers, there have also been changes. For example, before the 15th century the number "twenty" was designated as "two ten" (two dozen), but then it was reduced for faster pronunciation. Until the 15th century, the number "forty" was denoted by the word "four-thousand", and in the 15th-16th centuries this word was replaced by the word "forty", which originally meant a sack containing 40 squirrel or sable pelts. On the origin of the word "thousand" there are two options: from the old name "fat 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 the addition of a magnifying suffix to the number "millet" - a thousand (that is, denoted "the big one thousand"), it penetrated into Russian later, and before that the same value in Russian language was designated by the number "leodr". The word "billion" came into use only from the time of the Franco-Prussian War (1871), when the French had to pay Germany an indemnity of 5,000,000,000 francs. Like the "million" word "billion" comes from the root "one thousand" with the addition of the Italian magnifying suffix. In Germany and America for a while, the word "billion" meant a number of 100,000,000; This explains that the word billionaire in America was used before any of the rich had 1000 000 000 dollars. In the ancient (XVIII century.) Arithmetics of Magnitsky, a table of the names of numbers, reduced to the "quadrillion" (10 ^ 24, is given in the system through 6 digits). Perelman Ya.I. In the book "Entertaining arithmetic," the names of large numbers of that time differ somewhat from today: septillion (10 ^ 42), octalon (10 ^ 48), nonalon (10 ^ 54), decal (10 ^ 60), endecalon (10 ^ 66), dodecalon (10 ^ 72) and it is written that "there are no further names".

Principles of constructing names and a list of large numbers

All names of large numbers are constructed in a fairly simple way: in the beginning there is a Latin ordinal numeral, and in the end a suffix -illion is added to it. The exception is the name "million" which is the name of the number of one thousand (mille) and the magnifying suffix -illion. In the world there are two main types of names for large numbers:

  • System 3x + 3 (where x is the Latin ordinal number) - this system is used in Russia, France, USA, Canada, Italy, Turkey, Brazil, Greece
  • System 6x (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 ends with the suffix -illiard (we borrowed a billion from it, which is also called a billion).

Common list of numbers

Number Name Latin numerals Incrementing SI prefix Reducing the prefix SI Practical meaning
10 1 ten Deca- deci- Number of fingers on 2 hands
10 2 hundred hecto- Centi- Approximately 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 water bucket
10 9 Billion (billion) Duo (II) Giga- Nano- Estimated 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) Exa- Atto- 1/18 of the number of grains from the legendary award to the inventor of chess
10 21 Sextillion Sex (vi) Zetta- Cepto- 1/6 of the Earth's mass in tons
10 24 Septillion Septem (VII) Yotta- Yokto- The number of molecules in 37.2 liters of air
10 27 Octillion Octo (VIII) Una- (not approved) Sieve- (not approved) Half the mass of Jupiter in kilograms
10 30 quintillion Novem (IX) Dea- (not approved) Tredomo- (not approved) 1/5 of the number of all microorganisms on the planet
10 33 Decillion Decem (X) Una- (not approved) Revo- (not approved) Half the mass of the Sun in grams

The pronunciation of the numbers going on is often different.

Number Name Latin numerals Practical meaning
10 36 Andecillion Undecim (XI)
10 39 Duodecillion Duodecim (XII)
10 42 Tredcillion Tredecim (XIII) 1/100 of the number of air molecules on Earth
10 45 Quattradicillon Quattuordecim (XIV)
10 48 Quintecillion Quindecim (XV)
10 51 51 Sexdecillion Sedecim (XVI)
10 54 54 Septemecillion Septendecim (XVII)
10 57 Octodecyl So many elementary particles on the Sun.
10 60 Novemecillion
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 Quattro vigilion
10 78 Quinvigintillion
10 81 Sexigigillillion So many elementary particles in the universe
10 84 Septemigigillillion
10 87 Octovigilhillion
10 90 Novemigigillillion
10 93 Trigintillion Triginta (XXX)
10 96 96 Antiguintillion
    ...
  • 10 100 - googol (the figure was invented by the 9-year-old nephew of the American mathematician Edward Kasner)
  • ...
  • 10 123 - quadrigillillion (quadraginta, XL)
  • 10,153 quinquiginthillone (quinquaginta, L)
  • 10 183 - Sexagintilla (sexaginta, LX)
  • 10 213 - septuagintillion (septuaginta, LXX)
  • 10 243 - octogynthione (octoginta, LXXX)
  • 10 273 - nonagintilla (nonaginta, XC)
  • 10 303 - Centillion (Centum, C)

Further names can be obtained either directly or in the reverse order of the Latin numerals (as correctly, it is not known):

  • 10 306 - anthillillion or centunillion
  • 10 309 - duocentillione or centuo-one
  • 10 312 - trentillion or centrillion
  • 10 315 - quattcortillion or centavridillone
  • 10 402 - tri-tri-tintracentillione or centrate triglylione

I believe that the second variant of writing will be the most correct, since it more closely matches the construction of numerals in Latin and avoids ambiguities (for example, in the number of a trentillion, which, according to the first letter, is 10 903 and 10 312 ).

Numbers further:

  • 10 603 - ducentillion (ducenti, CC)
  • 10 903 - trecentillion (trecenti, CCC)
  • 10 1203 - quadringentillione (quadringenti, CD)
  • 10 1503 quingentillion (quingenti, D)
  • 10 1803 - sestcentillion (sescenti, DC)
  • 10 2103 - septingentión (DCC)
  • 10 2403 - octingentium (DCCC)
  • 10 2703 - nongenthyllione (nongenti, CM)
  • 10 3003 - a million (or milillion) (mille, M)
  • 10 6003 - duomilillion (duo milia, MM)
  • 10 9003 - Tremillion
  • 10 15003 - quinque milia
  • 10 308760 - ducentuille-doylum
  • 10 3000003 - miliamillionaion (decies centena milia)
  • 10 6000003 - duomiliamiliiumillion
  • 10 10 100 - gugolplex

Table of large numbers

Table of large numbers
One 1 = 10 0
Ten 10 = 10 1
Hundred 100 = 10 2
One thousand 1 000 = 10 3
10 000 = 10 4
100 000 = 10 5
Million 1 000 000 = 10 6
10 000 000 = 10 7
100 000 000 = 10 8
Billion (billion) 1 000 000 000 = 10 9
10 000 000 000 = 10 10
100 000 000 000 = 10 11
Trillion 1 000 000 000 000 = 10 12
10 000 000 000 000 = 10 13
100 000 000 000 000 = 10 14
Quadrillion 1 000 000 000 000 000 = 10 15
10 000 000 000 000 000 000 = 10 16
100 000 000 000 000 000 000 = 10 17
Quintillion 1 000 000 000 000 000 000 = 10 18
10 000 000 000 000 000 000 000 = 10 19
100 000 000 000 000 000 000 000 = 10 20
Sextillion 1 000 000 000 000 000 000 000 = 10 21
10 000 000 000 000 000 000 000 000 = 10 22
100 000 000 000 000 000 000 000 = 10 23
Seplillion 1 000 000 000 000 000 000 000 000 = 10 24
10 000 000 000 000 000 000 000 000 = 10 25
100 000 000 000 000 000 000 000 000 = 10 26
Octillion 1 000 000 000 000 000 000 000 000 000 = 10 27
10 000 000 000 000 000 000 000 000 000 = 10 28
100 000 000 000 000 000 000 000 000 000 = 10 29
Quintillion 1 000 000 000 000 000 000 000 000 000 000 = 10 30
10 000 000 000 000 000 000 000 000 000 000 = 10 31
100 000 000 000 000 000 000 000 000 000 000 = 10 32
Decillion 1 000 000 000 000 000 000 000 000 000 000 000 = 10 33

Literature

Perelman Ya.I. "Entertaining arithmetic." - Moscow: Triada-Litera, 1994, p. 134-140

Vygodsky M.Ya. "Handbook of elementary mathematics." - St.Petersburg, 1994, pp. 64-65

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

"Interestingly about physics and mathematics." - Kvant Library. No. 50. - Moscow: Nauka, 1988, p. 50