Names of numbers larger than a quadrillion are almost never used, for reasons discussed further below. It is debatable which of them should be considered real working English vocabulary and which are merely trivia, curiosities, or coinages. The following table lists those names of numbers which are found in many English dictionaries and thus have a special claim to being "real words". The "Traditional British" values shown are unused in American English and are largely obsolete in British English, but are dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America; see Long and short scales. Continental Europe, also referred to as mainland Europe or simply the Continent, is the continent of Europe, explicitly excluding European islands and, at times, peninsulas. ... Latin America consists of the countries of South America and some of North America (including Central America and some the islands of the Caribbean) whose inhabitants mostly speak Romance languages, although Native American languages are also spoken. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ...

The "standard dictionary numbers"

Apart from million, the words in this list ending with -illion are all derived by adding Latin prefixes (bi-, tri-, etc.) to the stem -illion.^[10] Centillion^[11] 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.).

All of the dictionaries included googol and googolplex, generally crediting it to the Kasner and Newman book and to Kasner's nephew. None include any higher names in the googol family (googolduplex, etc.). The Shorter Oxford English Dictionary comments that googol and googolplex are "not in formal mathematical use".

• In the book Fast Food Nation, author Eric Schlosser claims a Geographic Information System named "Quintillion" is used by McDonald's to analyze data to help predict a new location for one of its restaurants. According to Schlosser, Quintillion uses data such as satellite photos, income, new housing plans, and road layouts to predict future incomes and population patterns.^[12]

• The term Vigintillion was used by H. P. Lovecraft in his short stories The Call of Cthulhu and The Dunwich Horror.

For the film, see Fast Food Nation (film). ... Eric Schlosser (born 1959) is an American journalist and author. ... GIS redirects here. ... McDonalds Corporation (NYSE: MCD) is the worlds largest chain of fast-food restaurants, primarily selling hamburgers, chicken, french fries, milkshakes and soft drinks. ... Satellite imagery consists of photographs of Earth or other planets made from artificial satellites. ... Income, generally defined, is the money that is received as a result of the normal business activities of an individual or a business. ... House plans often come in the form of a set of construction or working drawings, although these are still sometimes called blueprints. ... Highway engineering is the process of design and construction of efficient and safe highways and roads. ... Demographics refers to selected population characteristics as used in government, marketing or opinion research, or the demographic profiles used in such research. ... This article is about the author. ... Cthulhu with the insane city Rlyeh in the background. ... The Dunwich Horror is a short story by H. P. Lovecraft. ...

Usage of names of large numbers

Some large numbers have real referents in human experience, and their names are encountered in many contexts. For example, on one day in 2004, Google News showed 78 600 hits on billion, starting with "Turkey Repays USD 1.6 Billion In Foreign Debt". It showed 9870 hits on trillion and 56 on quadrillion: for example, "The US Department of Energy reports that in 2002, the United States economy consumed 97.6 quadrillion BTUs (quad BTUs)." For other uses, see Number (disambiguation). ... The British thermal unit (BTU or Btu) is a unit of energy used in the Power, Steam Generation and Heating and Air Conditioning industry globally. ...

Names of larger numbers, however, have a tenuous, artificial existence. Although they may be found in dictionaries, these names are rarely found outside definitions, lists, and discussions of the ways in which large numbers are named. Even well-established names like sextillion are rarely used, since in the contexts of science, astronomy, and engineering, where large numbers often occur, numbers are usually written using scientific notation. In this notation, used since the 1800s, powers of ten are expressed as 10 with a numeric superscript, e.g., "The X-ray emission of the radio galaxy is 1.3·10⁴⁵ ergs." When a number such as 10⁴⁵ needs to be referred to in words, it is simply read out: "ten to the forty-fifth." This is just as easy to say, easier to understand, and less ambiguous than "quattuordecillion" (which means something different in the long scale and the short scale). When a number represents a quantity rather than a count, SI prefixes can be used; one says "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. Scientific notation, also known as standard form, is a notation for writing numbers that is often used by scientists and mathematicians to make it easier to write large and small numbers. ... An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... A parsec is the distance from the Earth to an astronomical object which has a parallax angle of one arcsecond. ... A light-year or lightyear (symbol: ly) is a unit of measurement of length, specifically the distance light travels in vacuum in one year. ... A barn (symbol b) is a unit of area. ...

Nevertheless, large numbers have an intellectual fascination and are of mathematical interest, and giving them names is one of the ways in which people try to conceptualize and understand them.

One of the first examples of this is The Sand Reckoner, in which Archimedes gave a system for naming large numbers. To do this, he called the numbers up to a myriad myriad (10⁸) "first numbers" and called 10⁸ itself the "unit of the second numbers". Multiples of this unit then became the second numbers, up to this unit taken a myriad myriad times, 10⁸·10⁸=10¹⁶. This became the "unit of the third numbers", whose multiples were the third numbers, and so on. Archimedes continued naming numbers in this way up to a myriad myriad times the unit of the 10⁸-th numbers, i.e., and embedded this construction within another copy of itself to produce names for numbers up to Archimedes then estimated the number of grains of sand that would be required to fill the known Universe, and found that it was no more than "one thousand myriad of the eighth numbers" (10⁶³.) The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. ... For other uses, see Archimedes (disambiguation). ...

Since then, many others have engaged in the pursuit of conceptualizing and naming numbers that really have no existence outside of the imagination. One motivation for such a pursuit is that attributed to the inventor of the word googol, who was certain that any finite number "had to have a name". Another possible motivation is competition between students in computer programming courses, where a common exercise is that of writing a program to output numbers in the form of English words.

It should be noted, too, that 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.

In this article, we present some names that have been given to large numbers, and the context and authority for the names. These numbers are almost pure mathematical abstractions, not physical realities. The names for such numbers are very rarely used. They may have a claim staked out for them in reference books, but they remain more in the nature of curiosities, trivia, or mathematical recreation than genuine working English vocabulary.

Adam, Chuquet and the origins of the "standard dictionary numbers"

The words 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: Image File history File links No higher resolution available. ... Jehan Adam was a French mathematician who flourished in the 15th century. ... Nicolas Chuquet (born 1445 (some sources say c. ... Estienne de La Roche (1470 - 1530) was a French mathematician Born in Lyon, the family of Estienne of the Rock, in addition to living in this city, has a property with Villefranche; having lived during its youth, Estienne is sometimes known under the name of Estienne de Villefranche. ... Estienne de La Roche (1470-1530) was a French mathematician. ...

Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers poit 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

(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).

Chuquet is sometimes credited with inventing the names million, billion, trillion, quadrillion, and so forth. This is an oversimplification.

• Million was certainly not invented by Adam or Chuquet. Milion is an Old French word thought to derive from Old Italian milione, an intensification of mille, a thousand. That is, a million is a big thousand, much as 1728 is a great gross.

• From the way in which Adam and Chuquet use the words, it can be inferred that they were recording usage rather than inventing it. One obvious possibility is that words similar to billion and trillion were already in use and well-known, but that Chuquet, an expert in exponentiation, extended the naming scheme and invented the names for the higher powers.

• Notice that Chuquet's names are only similar to, not identical to, the modern ones.

Adam and Chuquet used the long scale of powers of a million; that is, Adam's bymillion (Chuquet's byllion) denoted 10¹², and Adam's trimillion (Chuquet's tryllion) denoted 10¹⁸. A great gross is equal to a dozen gross, i. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ...

An aide-memoire

An easy way to find the value of the above numbers in the short scale is to take the number indicated by the prefix (such as 2 in billion, 4 in quadrillion, 18 in octodecillion, etc.), add one to it, and multiply that result by 3. For example, in a trillion, the prefix is tri, meaning 3. Adding 1 to it gives 4. Now multiplying 4 by 3 gives us 12, which is the power to which 10 is to be raised to express a short-scale trillion in scientific notation: one trillion = 10¹².

In the long scales, this is done simply by multiplying the number from the prefix by 6. For example, in a billion, the prefix is bi, meaning 2. Multiplying 2 by 6 gives us 12, which is the power to which 10 is to be raised to express a long-scale billion in scientific notation: one billion = 10¹².

These mechanisms are illustrated in the table in long and short scales. The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ...

The googol family

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,^[13] in the following passage: Edward Kasner (1878–1955), (City College of New York 1897; Columbia University M.A., 1897; Columbia University Ph. ...

Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with a hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex". A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, with so many zeros after the 1 that the number of zeros is a googol. This article is about the boxer, for the wrestler, see Primo Carnera. ... “Einstein” redirects here. ...

Value	Name	Authority
10100	Googol	Kasner and Newman, dictionaries (see above)
10googol =	Googolplex	Kasner and Newman, dictionaries (see above)

Conway and Guy ^[14] have suggested that N-plex be used as a name for 10^N. This gives rise to the name googolplexplex for 10^googolplex; however, the word googolplexian is given by one site. In addition, the terms googolduplex, googoltriplex, etc. have been coined by various persons for the numbers 10^googolplex, 10^googolduplex, etc.^{[citation needed]} Conway and Guy ^[14] 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. None of these names are in wide use, nor are any currently found in dictionaries. Not to be confused with Google, the Internet company, or the author Nikolai Gogol. ... This article is about a number. ... The reciprocal function: y = 1/x. ...

Extensions of the standard dictionary numbers

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This table illustrates several systems for naming large numbers, and shows how they can be extended past decillion. Image File history File links Question_book-3. ... Image File history File links Emblem-important. ...

Traditional British usage assigned new names for each power of one million (the long scale): 1000000 = 1 million, 1000000² = 1 billion, 1000000³ = 1 trillion and so on. It was adapted from French usage, and is similar to the system that was documented or invented by Chuquet. The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ... Nicolas Chuquet (born 1445 (some sources say c. ...

Traditional American usage (which, oddly enough, was also adapted from French usage but at a later date), and modern British usage, assigns new names for each power of one thousand (the short scale.) Thus, a billion is 1000 · 1000² = 10⁹, a trillion is 1000 · 1000³ = 10¹², and so forth. Due to its dominance in the financial world (and by the US-dollar) this was adopted for official United Nations documents. The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ... UN and U.N. redirect here. ...

Traditional French usage has varied; in 1948, France, which had been using the short scale, reverted to the long scale.

The term milliard is unambiguous and always means 10⁹. It is almost never seen in American usage, rarely in British usage, and frequently in European usage. The term is sometimes attributed to a French mathematician named 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. Jacques Peletier du Mans (1517 Le Mans – 1582 Paris) was a humanist, poet and mathematician of the French Renaissance. ... Events February 7 - Julius III becomes Pope. ... For other uses, see Latin (disambiguation). ...

With regard to 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. For example, as of 2004, Google searches on French-language pages for trillion, quadrillion, and quintillion return 6630, 312, and 127 hits respectively, whilst searches for trilliard and quadrilliard return only 102 and 7 hits respectively. However, one has to take into account that these large numbers are not often needed and that scientists almost always use scientific notation. In German the terms "Milliarde", "Billiarde" etc. are out of question. 2004 is a leap year starting on Thursday of the Gregorian calendar. ...

The naming procedure for large numbers is based on taking the number n occurring in 10³ⁿ⁺³ (short scale) or 10⁶ⁿ (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 = 10³⁰⁰⁰ (short scale) or 10^6·999 = 10⁵⁹⁹⁴ (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if n is 20 or smaller, and, for larger n (between 21 and 999), is due to John Horton Conway and Richard Guy. 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 have also proposed a consistent set of conventions which permit, in principle, the extension of this system to provide English names for any integer whatsoever.^[14] John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. ... Richard K. Guy is a Professor Emeritus in the Department of Mathematics at the University of Calgary. ...

Names of reciprocals of large numbers do not need to be listed here, because they are regularly formed by adding -th, e.g. quattuordecillionth, centillionth, etc.

For additional details, see Billion (disambiguation) and long and short scales. Look up billion in Wiktionary, the free dictionary. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ...

The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ... Jacques Peletier du Mans (1517 Le Mans – 1582 Paris) was a humanist, poet and mathematician of the French Renaissance. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ... Look up million in Wiktionary, the free dictionary. ... Look up million in Wiktionary, the free dictionary. ... Look up million in Wiktionary, the free dictionary. ... Billion may mean: 1,000,000,000 (one thousand million; ), used by most English-speaking countries (American and usual modern British meaning) 1,000,000,000,000 (one million million; ), used by most other countries outside Asia (older British meaning). ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ... Milliard is a French-derived word meaning the number 1,000,000,000 (109; one thousand million; SI prefix giga). ... Look up trillion in Wiktionary, the free dictionary. ... Billion may mean: 1,000,000,000 (one thousand million; ), used by most English-speaking countries (American and usual modern British meaning) 1,000,000,000,000 (one million million; ), used by most other countries outside Asia (older British meaning). ... Billion may mean: 1,000,000,000 (one thousand million; ), used by most English-speaking countries (American and usual modern British meaning) 1,000,000,000,000 (one million million; ), used by most other countries outside Asia (older British meaning). ... The quadrillion is a large number which has one of two values depending on how or where it is being used. ... Look up trillion in Wiktionary, the free dictionary. ... Look up trillion in Wiktionary, the free dictionary. ... The quadrillion is a large number which has one of two values depending on how or where it is being used. ... The quadrillion is a large number which has one of two values depending on how or where it is being used. ... Not to be confused with Google, the Internet company, or the author Nikolai Gogol. ... This article is about a number. ...

Other large numbers used in mathematics and physics

• Skewes' number
• Avogadro's number
• Graham's number
• Steinhaus–Moser notation

In number theory, Skewes number can refer to several extremely large numbers used by the South African mathematician Stanley Skewes. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ... Grahams number, named after Ronald Graham, is often described as the largest number that has ever been seriously used in a mathematical proof. ... In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers. ...

See also

This is a list of articles about numbers (not about numerals). ... Big numbers redirects here. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ... Nicolas Chuquet (born 1445 (some sources say c. ... Different cultures have different traditional numeral systems used for writing numbers and for naming large numbers. ... Jacques Peletier du Mans (1517 Le Mans – 1582 Paris) was a humanist, poet and mathematician of the French Renaissance. ... The traditional, ancient Indian numbering system, used today in India, Pakistan, Bangladesh,Nepal and Myanmar (Burma), is based on a unique grouping of 2 decimal places, rather than the 3 decimal places commonplace in the West (China, Korea, and Japan, for instance, use 4). ... An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ... Donald Knuth Donald Ervin Knuth (born January 10, 1938) is a renowned computer scientist and Professor Emeritus at Stanford University. ... An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... Billion may mean: 1,000,000,000 (one thousand million; ), used by most English-speaking countries (American and usual modern British meaning) 1,000,000,000,000 (one million million; ), used by most other countries outside Asia (older British meaning). ... Look up trillion in Wiktionary, the free dictionary. ... The English language has a number of words for indefinite and fictitious numbers - inexact terms of indefinite size, used for comic effect, for exaggeration, or when precision is unnecessary or undesirable. ... The term zillions can seriously mean all the possible -illions, as in million, billion, trillion, etc. ... A crore is a unit in the Indian numbering system, still widely used in Bangladesh, India, Myanmar, Sri Lanka, and Pakistan. ...

External links

• Large Numbers article by Robert Munafo
• How high can you count? by Landon Curt Noll.
• Full list of large number names list sorted by 10ⁿ and by word length
• Big numbers Educational site, which can name any numbers put into it (up to centillion)
• Name of numbers - tool for convert number to text

Landon Curt Noll (born 1960) [1] [2] is the discoverer of two Mersenne primes, which he found while still enrolled in high school and concurrently at Cal State Hayward [3]. He was also a member of the Amdahl Six [4] team which discovered another record prime in 1989; this prime...

References