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Names of large numbers

Названия больших чисел

Back in the fourth grade, I was interested in the question: “What are the numbers called over a billion? And why?”.

Since then, I have been searching for all the information on this issue for a long time and collecting it bit by bit. 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

The southern and eastern Slavic peoples used alphabetical numbering to write numbers. Moreover, not all letters played the role of numbers in Russians, but only those that are in the Greek alphabet. Above the letter denoting a number, a special “titlo” sign was placed. In this case, 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, Slavic numbering remained 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 have also changed. For example, until the 15th century, the number "twenty" was designated as "two ten" (two ten), but then decreased for faster pronunciation. Until the 15th century, the number “forty” was designated by the word “fourteen,” and in the 15th and 16th centuries this word was supplanted by the word “forty”, which originally denoted a sack 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 hundred" or from a modification of the Latin word centum - "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 big thousand"), it penetrated into the Russian language later, and before that the same meaning in Russian language was indicated 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 "thousand" with the addition of the Italian magnifying suffix. In Germany and America for some time the word "billion" meant the number 100 million; this explains that the word billionaire in America began to be used before any of the rich had $ 1,000,000,000. In the old (18th century) Magnitsky's "Arithmetic", a table of number names is brought up to the "quadrillion" (10 ^ 24, according to the system after 6 digits). Perelman Y.I. in the book "Entertaining Arithmetic" the names of large numbers of that time are slightly different from today: septillon (10 ^ 42), octalion (10 ^ 48), nonalion (10 ^ 54), decalion (10 ^ 60), endecalon (10 ^ 66), dodecalon (10 ^ 72) and it is written that "there are no further names."

Principles for constructing names and a 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 numeral, and at the end a million suffix is ​​added to it. An exception is the name "million" which is the name of the number thousand (mille) and the suffix "million". There are two main types of large number names in the world:

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

General list of numbers

Number Title Latin numeral SI prefix SI reducing prefix Practical value
10 1 ten soundboard deci- The number of fingers on 2 hands
10 2 hundred hecto- santi About half the number of all states on Earth
10 3 thousand kilo Milli- Estimated 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 Estimated Indian Population
10 12 trillion tres (III) tera pic- 1/13 of Russia's gross domestic product 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 number of grains from the legendary chess inventor award
10 21 sextillion sex (VI) zetta crypto 1/6 of 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) nea (not approved) sieve (not approved) Half the mass of Jupiter in kilograms
10 30 quintillion novem (IX) de- (not approved) thread (not approved) 1/5 of all microorganisms on the planet
10 33 decillion decem (X) un- (not approved) roar (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 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 quattorodecillion quattuordecim (xiv)
10 48 quindecillion quindecim (XV)
10 51 sex decillion sedecim (XVI)
10 54 septemdecillion septendecim (XVII)
10 57 octodecillion So many elementary particles in the sun
10 60 new decillion
10 63 vigintillion viginti (XX)
10 66 anvintintillion 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 sexwintillion So many elementary particles in the universe
10 84 septemvigintillion
10 87 octovigintillion
10 90 novemvigintillion
10 93 trigintillion triginta (XXX)
10 96 antrigintillion
    ...
  • 10 100 - googol (the number was invented by 9-year-old nephew of American mathematician Edward Kasner)
  • ...
  • 10 123 - quadraginta (quadraginta, XL)
  • 10 153 - quinquagintillion (quinquaginta, L)
  • 10 183 - sexagintillion (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 right, it is not known):

  • 10 306 - ancentillion or centunillion
  • 10 309 - duocentillion or centduollion
  • 10 312 - trententillion or centrillion
  • 10 315 - quattocentillion or centquadrillion
  • 10 402 - tertrigintatsentillion or centretrigintillion

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

Numbers further:

  • 10 603 - Duocentillion (ducenti, CC)
  • 10 903 - Trententillion (trecenti, CCC)
  • 10 1203 - quadringentillion (quadringenti, CD)
  • 10 1503 - quingentillion (quingenti, D)
  • 10 1803 - sescentillion (sescenti, DC)
  • 10 2103 - septingentillion (septingenti, DCC)
  • 10,2433 - octingentillion (octingenti, DCCC)
  • 10 2703 - nongentillion (nongenti, CM)
  • 10 3003 - one million (or one million) (mille, M)
  • 10,603 - duomillionaion (duo milia, MM)
  • 10 9003 - trillionillion
  • 10 15003 - quinque milillion (quinque milia)
  • 10 308760 - ducentduomiliananongendecillion
  • 10 3000003 - Millions (decies centena milia)
  • 10 6000003 - duomiliamilliaillion
  • 10 10 100 - googolplex

Large numbers table

Large 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 1,000,000,000,000,000,000,000,000 = 10 21
10,000,000,000,000,000,000,000 = 10 22
100,000,000,000,000,000,000,000 = 10 23
Seplillion 1,000,000,000,000,000,000,000,000,000 = 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 1,000,000,000,000,000,000,000,000,000,000 = 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 1,000,000,000,000,000,000,000,000,000,000,000 = 10 30
10,000,000,000,000,000,000,000,000,000,000 = 10 31
100,000,000,000,000,000,000,000,000,000,000,000 = 10 32
Decillion 1,000,000,000,000,000,000,000,000,000,000,000,000 = 10 33

Literature

Perelman I.I. "Entertaining arithmetic." - M .: Triad-Litera, 1994, p. 134-140

Vygodsky M.Ya. "Reference to elementary mathematics." - St. Petersburg., 1994, p. 64-65

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

“Interesting in physics and mathematics.” - Quantum Library. issue 50. - M .: Nauka, 1988, p. 50.