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Nevertheless, large numbers have an intellectual fascination and are of mathematical interest, and giving them names is one way people try to conceptualize and understand them. The names googol and googolplex inspired the name of the Internet company Google and its corporate headquarters, the Googleplex, respectively.
Googolplex's short scale name is derived from it equal to ten of the 3,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,332nd "-illion"s (This is the value of n when 10 × 10 (3n + 3) = 10 10 100) Thewords bymillion and trimillion were first recorded in 1475 in a manuscript of Jehan Adam. Subsequently, Nicolas Chuquet wrote a book Triparty en la science des nombres which was not published during Chuquet's lifetime. However, most of it was copied by Estienne de La Roche for a portion of his 1520 book, L'arismetique. Chuquet's book contains a passage in which he shows a large number marked off into groups of six digits, with the comment: Traditional British usage assigned new names for each power of one million (the long scale): 1,000,000 = 1 million; 1,000,000 2 = 1 billion; 1,000,000 3 = 1 trillion; and so on. It was adapted from French usage, and is similar to the system that was documented or invented by Chuquet.Concerning names ending in -illiard for numbers 10 6 n+3, milliard is certainly in widespread use in languages other than English, but the degree of actual use of the larger terms is questionable. The terms "Milliarde" in German, "miljard" in Dutch, "milyar" in Turkish, and "миллиард," milliard (transliterated) in Russian, are standard usage when discussing financial topics.
When preceding a component marked S or X, "tre" changes to "tres" and "se" to "ses" or "sex"; similarly, when preceding a component marked M or N, "septe" and "nove" change to "septem" and "novem" or "septen" and "noven". When a number represents a quantity rather than a count, SI prefixes can be used—thus " femtosecond", not "one quadrillionth of a second"—although often powers of ten are used instead of some of the very high and very low prefixes. In some cases, specialized units are used, such as the astronomer's parsec and light year or the particle physicist's barn. Names of numbers above a trillion are rarely used in practice; such large numbers have practical usage primarily in the scientific domain, where powers of ten are expressed as 10 with a numeric superscript. However, these somewhat rare names are considered acceptable for approximate statements. For example, the statement "There are approximately 7.1 octillion atoms in an adult human body" is understood to be in short scale of the table below (and is only accurate if referring to short scale rather than long scale). Most names proposed for large numbers belong to systematic schemes which are extensible. Thus, many names for large numbers are simply the result of following a naming system to its logical conclusion—or extending it further. [ citation needed] Origins of the "standard dictionary numbers" [ edit ]Traditional American usage (which was also adapted from French usage but at a later date), Canadian, and modern British usage assign new names for each power of one thousand (the short scale.) Thus, a billion is 1000 × 1000 2 = 10 9; a trillion is 1000 × 1000 3 = 10 12; and so forth. Due to its dominance in the financial world (and by the US dollar), this was adopted for official United Nations documents. Or if you prefer the first mark can signify million, the second mark byllion, the third mark tryllion, the fourth quadrillion, the fifth quyillion, the sixth sixlion, the seventh septyllion, the eighth ottyllion, the ninth nonyllion and so on with others as far as you wish to go). Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers point tryllion Le quart quadrillion Le cinq e quyllion Le six e sixlion Le sept. e septyllion Le huyt e ottyllion Le neuf e nonyllion et ainsi des ault' s se plus oultre on vouloit preceder
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. These naming procedures are based on taking the number n occurring in 10 3 n+3 (short scale) or 10 6 n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion. Names of larger numbers, however, have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of how large numbers are named. Even well-established names like sextillion are rarely used, since in the context of science, including astronomy, where such large numbers often occur, they are nearly always written using scientific notation. In this notation, powers of ten are expressed as 10 with a numeric superscript, e.g. "The X-ray emission of the radio galaxy is 1.3 ×10 45joules." When a number such as 10 45 needs to be referred to in words, it is simply read out as "ten to the forty-fifth" or "ten to the forty-five". This is easier to say and less ambiguous than "quattuordecillion", which means something different in the long scale and the short scale. Ten trillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentilliduotrigintatrecentillionTen millisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentilliard Since the system of using Latin prefixes will become ambiguous for numbers with exponents of a size which the Romans rarely counted to, like 10 6,000,258, Conway and Guy co-devised with Allan Wechsler the following set of consistent conventions that permit, in principle, the extension of this system indefinitely to provide English short-scale names for any integer whatsoever. [15] The name of a number 10 3 n+3, where n is greater than or equal to 1000, is formed by concatenating the names of the numbers of the form 10 3 m+3, where m represents each group of comma-separated digits of n, with each but the last "-illion" trimmed to "-illi-", or, in the case of m = 0, either "-nilli-" or "-nillion". [15] For example, 10 3,000,012, the 1,000,003rd "-illion" number, equals one "millinillitrillion"; 10 33,002,010,111, the 11,000,670,036th "-illion" number, equals one "undecillinilliseptuagintasescentillisestrigintillion"; and 10 29,629,629,633, the 9,876,543,210th "-illion" number, equals one "nonilliseseptuagintaoctingentillitresquadragintaquingentillideciducentillion". [15] John Horton Conway and Richard K. Guy [15] have suggested that N-plex be used as a name for 10 N. This gives rise to the name googolplexplex for 10 googolplex = 10 10 10 100. Conway and Guy [15] have proposed that N-minex be used as a name for 10 −N, giving rise to the name googolminex for the reciprocal of a googolplex, which is written as 10 -(10 100). None of these names are in wide use.
The term milliard is unambiguous and always means 10 9. It is seldom seen in American usage and rarely in British usage, but frequently in continental European usage. The term is sometimes attributed to French mathematician Jacques Peletier du Mans circa 1550 (for this reason, the long scale is also known as the Chuquet-Peletier system), but the Oxford English Dictionary states that the term derives from post-Classical Latin term milliartum, which became milliare and then milliart and finally our modern term. The names googol and googolplex were invented by Edward Kasner's nephew Milton Sirotta and introduced in Kasner and Newman's 1940 book Mathematics and the Imagination [14] in the following passage: All of the dictionaries included googol and googolplex, generally crediting it to the Kasner and Newman book and to Kasner's nephew (see below). None include any higher names in the googol family (googolduplex, etc.). The Oxford English Dictionary comments that googol and googolplex are "not in formal mathematical use".The naming procedure for large numbers is based on taking the number n occurring in 10 3 n+3 (short scale) or 10 6 n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion. In this way, numbers up to 10 3·999+3=10 3000 (short scale) or 10 6·999=10 5994 (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if n is 9 or smaller. For larger n (between 10 and 999), prefixes can be constructed based on a system described by Conway and Guy. [15] Today, sexdecillion and novemdecillion are standard dictionary numbers and, using the same reasoning as Conway and Guy did for the numbers up to nonillion, could probably be used to form acceptable prefixes. The Conway–Guy system for forming prefixes: Apart from million, the words in this list ending with - illion are all derived by adding prefixes ( bi-, tri-, etc., derived from Latin) to the stem - illion. [11] Centillion [12] appears to be the highest name ending in -"illion" that is included in these dictionaries. Trigintillion, often cited as a word in discussions of names of large numbers, is not included in any of them, nor are any of the names that can easily be created by extending the naming pattern ( unvigintillion, duovigintillion, duoquinquagintillion, etc.). Adam and Chuquet used the long scale of powers of a million; that is, Adam's bymillion (Chuquet's byllion) denoted 10 12, and Adam's trimillion (Chuquet's tryllion) denoted 10 18. Indian and Pakistani English do not use millions, but have their own system of large numbers including lakhs (Anglicised as lacs) and crores. [1] English also has many words, such as "zillion", used informally to mean large but unspecified amounts; see indefinite and fictitious numbers.
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