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Large numbers

Названия больших чисел

Back in fourth grade, I was interested in the question: "What are the names of more than a billion numbers? And why?".

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

Now I present all the information I have found so that others can answer the question: "What are the names of large and very large numbers?".

Story

Southern and Eastern Slavic peoples used alphabetic numbering to write numbers. Moreover, Russians didn’t play the role of numbers not all letters, but only those that are in the Greek alphabet. Above the letter denoting the number, put a special icon "titlo". 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 is preserved until the end of the 17th century. Under Peter I, the so-called "Arabic numbering" prevailed, which we still use today.

The names of the numbers also changed. For example, until the 15th century, the number “twenty” was designated as “two ten” (two dozen), but then declined for faster pronunciation. Until the 15th century, the number "forty" was designated by the word "fourties", and in the 15-16th centuries this word was supplanted by the word "forty", which originally meant a bag in which 40 squirrel or sable skins were placed. On the origin of the word "thousand" there are two options: from the old name "thick 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" - one thousand (i.e. it meant "big thousand"), it penetrated into Russian later, and before that the same value n was designated by the number "leodr." The word "billion" came into use only from the time of the Franco-Prussia war (1871), when the French had to pay Germany a contribution of 5,000,000,000 francs. Like "million," the word "billion" comes from the root of "one 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 in America was used before any of the rich had 1,000,000,000 dollars. In the old (XVIII century) Magnitsky's "Arithmetic", a table of the names of numbers, brought to the "quadrillion" (10 ^ 24, according to the system after 6 digits) is given. Perelman Ya.I. in the book "Entertaining Arithmetic" are the names of large numbers of that time, slightly different from today's: septillon (10 ^ 42), octalion (10 ^ 48), nonalon (10 ^ 54), decalion (10 ^ 60), endecalion (10 ^ 66), the dodecalion (10 ^ 72) and it is written that “there are no further names”.

Principles of building names and a list of large numbers

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

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

General list of numbers

Number Title Latin numeral SI increasing prefix SI Reducing Console Practical meaning
10 1 ten deca deci- The number of fingers on 2 hands
10 2 hundred hecto- centi Approximately half the number of all states on Earth
10 3 thousand kilo- Milli- Approximate number of days at 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- Estimated population of india
10 12 trillion tres (III) tera- pico 1/13 of Russia's gross domestic product in rubles for 2003
10 15 quadrillion quattor (IV) peta femto 1/30 of the length of the parsec 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 chaining 1/6 of 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) non- (not approved) sieve- (not approved) Half the mass of Jupiter in kilograms
10 30 quintillion novem (ix) de- (not approved) tredo (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 that follow is often different.

Number Title Latin numeral Practical meaning
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 seksdetsillionion sedecim (XVI)
10 54 septemdecillion septendecim (XVII)
10 57 octodecillion So many elementary particles on the sun
10 60 new million
10 63 vigintillion viginti (XX)
10 66 Anvigintillion unus et viginti (XXI)
10 69 dovigintillion duo et viginti (XXII)
10 72 trevigtiillion tres et viginti (XXIII)
10 75 quattorvigintillion
10 78 quinvigintillion
10 81 sexvigintillion So many elementary particles in the universe
10 84 septemvigintiillion
10 87 octowingtillion
10 90 newmvintillion
10 93 trigintillion triginta (XXX)
10 96 antrigintillion
    ...
  • 10 100 - googol (the number came up with 9-year-old nephew of American mathematician Edward Kasner)
  • ...
  • 10 123 - quadragintillion (quadraginta, XL)
  • 10,153 - Quinquaginta (L)
  • 10 183 - sexintillion (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 (it is not known how correctly):

  • 10 306 - acenthene or centuninlion
  • 10 309 - duocentillion or centduollyon
  • 10 312 - tretsentiillion or centrillion
  • 10 315 - Quartorcentillion or centquadrillion
  • 10,402 - tertrigintacentillion or centretrigrintillion

I believe that the second spelling would be most appropriate, since it more closely matches the construction of numerals in Latin and avoids ambiguities (for example, among the trocentillion, which in the first spelling is both 10,903 and 10,312).

Numbers further:

  • 10,603 - ducentillion (ducenti, CC)
  • 10,903 - trecentillion (trecenti, CCC)
  • 10 1203 - quadringenthene (quadringenti, CD)
  • 10 1503 - quingentillion (quingenti, D)
  • 10 1803 - session centrillion (sescenti, DC)
  • 10 2103 - septingentillion (septingenti, DCC)
  • 10 2403 - Octingentillion (octingenti, DCCC)
  • 10 2703 - nongentillion (nongenti, CM)
  • 10,303 - one million (or million) (mille, M)
  • 10,603 - duomilyallion (duo milia, MM)
  • 10 9003 - tremillillion
  • 10 15003 - quinque milia
  • 10 308760 - ducendomilianongentnovdecillion
  • 10 3000003 - Milami lillion (decies centena milia)
  • 10 6000003 - duomiliamilyonillion
  • 10 10 100 - googolplex

Big numbers table

Big numbers table
One 1 = 10 0
Ten 10 = 10 1
Hundred 100 = 10 2
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 = 10 16
100,000,000,000,000,000 = 10 17
Quintillion 1 000 000 000 000 000 000 = 10 18
10,000,000,000,000,000,000 = 10 19
100,000,000,000,000,000,000 = 10 20
Sextillion 1 000 000 000 000 000 000 000 = 10 21
10,000,000,000,000,000,000,000 = 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 = 10 30
10 000 000 000 000 000 000 000 000 000 = 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 I.I. "Entertaining arithmetic". - M .: Triad-Litera, 1994, pp. 134-140

Vygodsky M.Ya. "Elementary Mathematics Handbook". - St. Petersburg, 1994, pp. 64-65

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

"Interestingly about physics and mathematics." - The Quantum Library. issue 50. - M .: Science, 1988, p. 50