Names for Large Numbers Using the Dictionary Names for Large Numbers The English names for large numbers are coined from the Latin names for small numbers n by adding the ending -illion suggested by the name "million." Thus billion and trillion are coined from the Latin prefixes bi- (n = 2) and tri- (n = 3), respectively. In the American system for naming large numbers, the name coined from the Latin number n applies to the number 103n+3. In a system traditional in many European countries, the same name applies to the number 106n. In particular, a billion is 109 = 1 000 000 000 in the American system and 1012 = 1 000 000 000 000 in the European system. For 109, Europeans say "thousand million" or "milliard." Although we describe the two systems today as American or European, both systems are actually of French origin.

The French physician and mathematician Nicolas Chuquet (1445-1488) apparently coined the words byllion and tryllion and used them to represent 1012 and 1018, respectively, thus establishing what we now think of as the "European" system. However, it was also French mathematicians of the 1600's who used billion and trillion for 109 and 1012, respectively. This usage became common in France and in America, while the original Chuquet nomenclature remained in use in Britain and Germany. The French decided in 1948 to revert to the Chuquet ("European") system, leaving the U.S. as the chief standard bearer for what then became clearly an American system. In recent years, American usage has eroded the European system, particularly in Britain and to a lesser extent in other countries. This is primarily due to American finance, because Americans insist that $1 000 000 000 be called a billion dollars.

In 1974, the government of Prime Minister Harold Wilson announced that henceforth "billion" would mean 109 and not 1012 in official British reports and statistics. The Times of London style guide now defines "billion" as "one thousand million, not a million million." The result of all this is widespread confusion. Anyone who uses the words "billion" and "trillion" internationally should make clear which meaning of those words is intended. On the Internet, some sites outside the U.S. use the compound designation "milliard/billion" to designate the number 1 000 000 000. In science, the names of large numbers are usually avoided completely by using the appropriate SI prefixes . Thus 109 watts is a gigawatt and 1012 joules is a terajoule. Such terms cannot be mistaken. There is no real hope of resolving the controversy in favor of either system. Americans are not likely to adopt the European nomenclature, and Europeans will always regard the American system as an imposition.

However, it is possible to imagine a solution: junk both Latin-based systems and move to a Greek-based system in which, for n > 3, the Greek number n is used to generate a name for 103n. (The traditional names thousand and million are retained for n = 1 and 2 and the special name gillion, suggested by the SI prefix giga-, is proposed for n = 3.) n = triacontatrillion This process can be continued indefinitely, but one has to stop somewhere. The name centillion (n = 100) has appeared in many dictionaries. A centillion is 10303 (1 followed by 303 zeroes) in the American system and a whopping 10600 (1 followed by 600 zeroes) in the European system. Finally, there is the googol , the number 10100 (1 followed by 100 zeroes). Invented more for fun than for use, the googol lies outside the regular naming systems.

The googol equals 10 duotrigintillion in the American system, 10 sexdecilliard in the European system, and 10 triacontatrillion in the proposed Greek-based system. The googolplex (1 followed by a googol of zeroes) is far larger than any of the numbers discussed here. Return to the Dictionary Contents page . You are welcome to email the author (rowlett@email.unc.edu) with comments and suggestions. All material in this folder is copyright &COPY; 2001 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. November 1, 2001 Google (number) - definition of Google (number) by The Free Dictionary Google (number) - definition of Google (number) by The Free Dictionary Also found in: Thesaurus , Encyclopedia , Wikipedia .

Related to Google (number): googol goo·gol (go͞o′gôl′, -gəl) n. The number 10 raised to the power 100 (10100), written out as the numeral 1 followed by 100 zeros. [Coined at the age of nine by Milton Sirotta, nephew of Edward Kasner (1878-1955), American mathematician.] googol (Mathematics) the number represented as one followed by 100 zeros (10100) [C20: coined by E. Kasner (1878–1955), American mathematician] goo•gol n. a number that is equal to 1 followed by 100 zeros, expressed as 10100. [1935–40; introduced by U.S.

mathematician Edward Kasner (1878–1955), whose nine-year-old nephew allegedly invented it] goo·gol (go͞o′gôl′, go͞o′gəl) The number 10 raised to the 100th power, written as 10100 or as 1 followed by 100 zeros. googol - Coined when mathematician Edward Kasner asked his nephew to create a word for the number 1 followed by 100 zeros. See also related terms for zero . ThesaurusAntonymsRelated WordsSynonymsLegend: Noun 1. googol - a cardinal number represented as 1 followed by 100 zeros (ten raised to the power of a hundred) cardinal number , cardinal - the number of elements in a mathematical set; denotes a quantity but not the order Translations Googol | Definition of Googol by Merriam-Webster See googol defined for kids google vs. googol The verb google and the noun googol are commonly confused because they have similar pronunciations.

Google is the word that is more common to us now, and so it is sometimes mistakenly used as a noun to refer to the number 10100. That number is a googol , so named by Milton Sirotta, the nephew of the American mathematician Edward Kasner, who was working with large numbers like 10100. Google , on the other hand, is the name of a search engine as well as a verb that refers to searching the Internet using the Google search engine. (The search engine’s name was inspired by the number: the founders of Google chose the name to reflect their mission “to organize a seemingly infinite amount of information on the web.”) You can remember that the number is spelled googol by remembering that a googol has lots of o’s. Two related words, googolplex and googleplex, are also commonly confused. A googolplex is the number 1 followed by a googol of zeros; the Googleplex is the Mountain View, California headquarters of Google. Did You Know?

Around 1930, American mathematician Edward Kasner found himself working with numbers as large as 10 to the 100th power - that's a one followed by 100 zeroes. While it is possible to write that number using standard scientific notation, Dr. Kasner felt that it deserved a name of its own. According to his own account, Dr. Kasner asked his nine-year-old nephew, Milton Sirotta, to pick a name, promising the boy that he would use the word in the future. Milton made up the word googol, and so the enormous number was christened. Dr. Kasner kept his promise, and the word has spread and been widely adopted by mathematicians and the general public alike.

Origin and Etymology of googol coined by Milton Sirotta b ab 1929 nephew of Edward Kasner †1955 American mathematician First Known Use: 1937 The numbers *Googol* and *Googolplex* at MROB Search: The numbers Googol and Googolplex (You might also wish to view googol and googolplex in context on my numbers page; or on my large numbers page as examples of class 2 and class 3 numbers; and to make calculations involving these numbers, use Hypercalc .) Googol 1×10100 = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000 10100 can be called "ten duotrigintillion" by the standard Chuquet system , but is better known by the name googol.

This is perhaps the best-known example of a number that was "invented" just for the purpose of being large. Only slightly less well-known is the much larger googolplex . History Mathematician Edward Kasner [2] asked his nephew Milton Sirotta (who was 9 years old at the time) to invent a name for the number 1 with a hundred zeros written after it, and the nephew chose the name "googol". As Kasner's telling of the story goes, He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. The name "googolplex" was invented at the same time, and also by Milton Sirotta if we trust the grammatical implication of the wording in [2] . An article by Carl Bialik [6] gives more background and suggests a date for the invention of these words being in the 1920's. Regarding its definition, Kasner wrote: It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. [...] It would never do to have [contemporary boxing champion Primo] Carnera [be] a better mathematician than Dr.

Einstein , simply because he had more endurance. [and so it was decided that googolplex should be] a specific finite number, with so many zeros after the 1 that the number of zeros is a googol.  Edward Kasner [2] A generation later, googol had been popularized enough to be able to reach audiences of the widely-distributed Peanuts comic strip in which Schroeder estimates Lucy's odds of eventually marrying him as "Oh, I'd say about 'googol' to one": Schroeder and Lucy discuss googol This Peanuts strip (first run on January 23, 1963) easily broke the record for the largest number explicitly written out in a mainstream comic strip, although I suspect that may have been surpassed recently by the nerd-friendly populist Foxtrot. If you don't care about type of representation, then the current record-holder would probably be the 3rd panel of xkcd 207 .

(There are many other poetry and lyric references on my main numbers pages including 525600 , 8675309 , 1010 , 1011 , 1027 and 1010000000000 .) Carl Sagan tells of the invention of Googol in the 1980 TV series Cosmos, then goes on to discuss googolplex . The name of the company Google derives from "googol". The choice of a name for the search engine (a name change from the earlier "BackRub", which referred to URL "back links") was an intentional allusion to the large number; this "fit well with [the] goal of building very large-scale search engines" (in the words of its founders according to [7] ). Googol Learning Enterprises uses birdlike puppet characters called "Googols" to teach children about mathematics and related topics. Their What's a Googol? page has a video of two of them teaching the meanings of Googol, Googolplex and Infinity.

Googol in Popular Culture There are many references to googol in popular culture (most are since the late 1990's). The following examples are from the Wikipedia page on googol as it existed in early 2010: Googol was the answer to the million- pound question: "A number one followed by 100 zeros is known by what name?" on Who Wants to Be a Millionaire? when Major Charles Ingram attempted to defraud the quiz show on 10 September 2001. The other options were a megatron , a gigabit or a nanomole . In Back to the Future III , Emmett Brown states that Clara was "One in a googolplex". In Steve Martin 's comedy album Comedy Is Not Pretty! , Martin talks about buying a googolphonic stereo system (which he erroneously describes as having, "the highest number of speakers before infinity...") after not being satisfied with his stereophonic , quadraphonic , then dodecaphonic systems.

In an episode{{Which?|date=November 2009}} of Samurai Jack , the shape-shifting master of darkness Aku puts a price on the noble samurai's head of 2 googolplex. In a March 1976 comic book issue of Richie Rich (Vaults of Mystery #9), introduced a villain named "The Googol". In 2002 the band Clutch released their album Live At The Googolplex. On Phineas & Ferb , Danville's main shopping center is the Googolplex Mall.

In The Simpsons animated television series the large cinema in Springfield is known as the "googolplex" Googolplex 1010100 = 1010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 For many people, Googolplex is the largest number with a name. Like googol it is a number that was "invented" just for the purpose of being large. As described under the googol entry, credit for the invention of the -plex suffix is indeterminate. See [4] for more about this number. In the 1980 TV series Cosmos , in the episode called Lives of the Stars*, Carl Sagan spends some time talking about large numbers.

He points out that googolplex has so many zeros that there is not enough room to write out all the zeros even in the entire volume of the known universe, and also comments that "A googolplex is precisely as far from infinity as the number one". [3] . Google 's headquarters in California is referred to as the Googleplex, an inside joke and etymological back-formation (see above ). In The Simpsons, the family sometimes sees a movie at the "Springfield Googolplex" theatres, a humorous reference to multiplex, megaplex, and the general trend towards theatres with more screens (each of which is often smaller). Carrying the idea to a ( fictitious ) extreme, the G∞golplex Theaters website 1 suggests that each patron can see a different movie through the use of virtual reality headsets: Googolplex Theaters was founded in Milwaukee, Wisconsin in 1994 by visionary cinema mogul Bob Googol. Recognizing the trend toward placing ever-more screens under one roof, he conceived of a theater where the number of screens was limited only by the number of patrons.

Most googol-lore comes from the number's appeal as a representative huge number; see my large numbers page for many more including the Skewes numbers , the mega and moser , and the Graham-Rothschild number . Physical Interpretation Fred Adams of the University of Michican explains that the heat-death of the universe would take at least as long as the evaporation time of the largest black holes. Since the largest black holes (with "the mass of a galaxy") would take 1098 years to evaporate, Adams says that "a good bet" for the time until the heat-death of the universe is about 10100 years (see Future of an expanding universe ). Googolplex is a number far too big to relate to anything physical  or is it? Many large numbers come up in the study of combinations, such as the number of ways to shuffle a deck of 52 cards ( 8.065817...×1067 ) or the number of ways to arrange 5.9 billion nucleotide base-pairs into 46 chromosomes ( 3.01607×103576838408 ).

A combinatoric interpretation is perhaps the easiest way to approach a physical interpretation of googolplex. Just after introducing googol and googolplex and their definitions, Kasner and Newman [2] contemplate the odds of a book, suspended from a person's hand by a string, spontaneously jumping up into the hand by cooperative action of the Brownian motion of many individual molecules in the surrounding air. The odds of such an event happening during one's lifetime is given as "between 1/googol and 1/googolplex". More recently, through the work of Stephen Hawking and many others, it has been possible to make more precise definitions of combinatoric numbers involving large physical objects such as stars, black holes and galaxies. The following description comes from Don Page via Frank Pilhofer [4] , and is highly paraphrased: Quantum physicists talk about distinct and indistinct states, overlapping wave functions and many other things. One of the important principles of such " quantum indeterminacy " concerns how much time it takes for a system with many possible states to spontaneously assume a certain, given state.

For simplicity it is imagined that the "system" (usually some set of particles) is inside an impermeable, rigid box (to prevent anything from going in or out, even "information" or a "measurement" in the quantum mechanical sense). If you're outside the box you have no idea what's inside, and any state can spontaneously occur (even a higher-energy state). For example, if the system is a proton and an electron, the possible states include: A hydrogen atom, a hydrogen atom with the electron in a higher "shell", a separate proton and electron, a neutron, or many other things. The amount of time you might have to wait for one of these states to occur depends on the number of possible states, which depends on the number of particles inside. Cosmologists and physicists often use these concepts to discuss what might happen inside black holes. In practical terms the inside of a black hole is isolated from us (nothing can get out), but for this thouht experiment we still place it inside a rigid nonpermeable box, so that nothing new goes into the system, and ensuring that all Hawking radiation remains in the system.

Like any other isolated system, one can talk about all the possible states that might exist and how long it might take for a certain state to arise. In theory, the contents of the box will at some point in the future cease to be a black hole and instead be real matter. The formula for the number of possible states is a really big exponential function with Planck constants in it and other such things. To get a googolplex states, we need a black hole with a mass about 4.685×1011 times that of the Sun. This mass is conveniently just about equal to that of the Milky Way Galaxy (see [5] or Wikipedia). The number of states of such a black hole is somewhere around a googolplex, and in a comparable amount of time it would be expected to take on all possible states. It's such a big number that it doesn't even matter what units you use  a googolplex seconds, a googolplex millennia, or whatever  is the amount of time you'd have to wait for the contents of an impermeable, rigid box containing a black hole with the mass of the Milky Way to spontaneously become identical to the actual Milky Way as we know it.

Other Names The Conway-Wechsler naming system gives names to all powers of 10 beyond the standard names like million and decillion.

Using that naming system, a googol is "ten duotrigintillion", and a googolplex has the rather formidable name "ten trilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli

­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­trestriginta­trecentilli­duotriginta­trecentillion.

"googolplexplex" It is natural to think of the -plex at the end of googolplex as being a suffix that means "10 to the power of" whatever the suffix has been added to. That implies names like millionplex for 101000000 and googolplexplex for 101010100. Googol and Googolplex as examples of "power towers" Googol, 10100, can also be expressed 10102, (1010)10, or 10④3 using the lower hyper4 operator . It is an example of a " class-2 number " under the system I describe on my large numbers page . Googolplex, 1010100, can also be expressed 1010102 or 10④101. It is an example of a class-3 number .

Footnotes 1 : (a creation of Kelson Vibber, at his "Hyperborea" website and formerly at Bibliography [2] Kasner and Newman, Mathematics and the Imagination, (Simon and Schuster, New York) 1940 (also republished in 1989 and in 2001). The story can also be found online  search for Googol plus the leading sentence "Words of wisdom are spoken by children at least as often as by scientists." [3] Carl Sagan, Ann Druyan and Steven Soter (creators), Cosmos: a Personal Voyage (television series), 1980. The first several minutes of episode 9 discusses googol and googolplex; it may be available here: Lives of the Stars .

[4] Pilhofer, Frank, Googolplex and How to get a Googolplex (web pages), 1999 (updated in 2002) (old URL was ~fp/Tools/GetAGoogol.html) Googol - definition of googol by The Free Dictionary Googol - definition of googol by The Free Dictionary Related to googol: googolplex , Googolplexian goo·gol (go͞o′gôl′, -gəl) n. The number 10 raised to the power 100 (10100), written out as the numeral 1 followed by 100 zeros. [Coined at the age of nine by Milton Sirotta, nephew of Edward Kasner (1878-1955), American mathematician.] googol (Mathematics) the number represented as one followed by 100 zeros (10100) [C20: coined by E. Kasner (1878–1955), American mathematician] goo•gol n.

a number that is equal to 1 followed by 100 zeros, expressed as 10100. [1935–40; introduced by U.S. mathematician Edward Kasner (1878–1955), whose nine-year-old nephew allegedly invented it] goo·gol (go͞o′gôl′, go͞o′gəl) The number 10 raised to the 100th power, written as 10100 or as 1 followed by 100 zeros. googol - Coined when mathematician Edward Kasner asked his nephew to create a word for the number 1 followed by 100 zeros. See also related terms for zero . ThesaurusAntonymsRelated WordsSynonymsLegend: Noun 1.

googol - a cardinal number represented as 1 followed by 100 zeros (ten raised to the power of a hundred) cardinal number , cardinal - the number of elements in a mathematical set; denotes a quantity but not the order Translations Googol, googolplex — & Google By Ryan Goodrich, LiveScience Contributor | May 13, 2013 07:36pm ET MORE A googol equals 1 followed by 100 zeros. Googol is a mathematical term to describe a huge quantity. It is not an incorrect spelling of the search engine giant’s name, Google — actually, it's the other way around. Googol, a quantity that surpasses even the number of hydrogen atoms in the observable universe, is a number dating back to the mid-1900s and is still used by mathematicians today. Silly name for a silly sum Googol is the label for 10 to the hundredth power (10100), or 1 followed by 100 zeros .

Invented by Edward Kasner, the American mathematician referenced the quantity extensively in his 1940 book, "Mathematics and the Imagination." Kasner intended the number to serve as an example for students in showing how a number could be so incredibly large, it could baffle their minds. While the term wasn’t more universally accepted and used until his book’s publishing, Kasner dated its creation to 1920 when he asked his 9-year-old nephew, Milton Sirotta, what he should call the number. Milton appropriately responded that such a silly sum required an equally silly name, from which the term "googol" was coined. Googolplex After naming googol, Milton proposed the further term of "googolplex," describing it as “one, followed by writing zeros until you get tired.” Rather than gauging a mathematician’s skill by their endurance in writing zeros, Kasner adopted a more formal interpretation of 10 followed by googol zeros, as opposed to a googol’s 100 zeros.

To quantify a googolplex, astronomer and astrophysicist Carl Sagan gave the example of filling the entire volume of the observable universe with fine dust particles roughly 1.5 micrometers in size. From this, the total number of different combinations in which these particles could be arranged would equal approximately one googolplex. Ginormous numbers For its time, googol was the largest known number. Since the invention of the supercomputer, even larger numbers can be easily calculated, such as Graham’s number or Skewes’ number. For example, a centillion, a one and 303 zeros, is one of many large numbers. While the creation and naming of such large numbers is readily possible for any non-mathematician, their invention requires a specific purpose as opposed to an arbitrary notion. Neither googol nor googolplex truly has any mathematical significance beyond acting as reference points for visualizing large numbers. For example, such numbers are used to speculate on things like the number of particles in the universe, the total number of chess game variances possible, or even 70 factorial.

In other words, numbers as large as, even larger than, googols and googolplexes are used to quantify potential rather than physical things, thus increasing the potential application. In mathematical circles, their use is likely to be much more often than in everyday life, and only to quantify extremely large bodies of data. Googol and Google Larry Page and Sergey Brin, two of the founders of Google, grew up fascinated with mathematics and decided to name their company after the number. As the early Google team searched available domain names, the Stanford graduate student at the computer accidentally typed googol as “google” and the name stuck. While Google is a misspelling of googol, the company is based upon the same mathematical principles, choosing even to name Google’s headquarters in Mountain View as Googleplex. Related: Googol | Define Googol at Dictionary.com googol [goo-gawl, -gol, -guh l] /ˈgu gɔl, -gɒl, -gəl/ Spell noun 1. a number that is equal to 1 followed by 100 zeros and expressed as 10 100 .

Origin of googol 1935-40; introduced by U.S. mathematician Edward Kasner (1878-1955), whose nine-year-old nephew allegedly invented it Can be confused British Dictionary definitions for googol Expand the number represented as one followed by 100 zeros (10100) Word Origin C20: coined by E. Kasner (1878–1955), American mathematician Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012 Word Origin and History for googol Expand n. 1940, in "Mathematics and the Imagination," a layman's book on mathematics written by U.S. mathematicians Edward Kasner (1878-1955) and James R.

Newman, the word supposedly coined a year or two before by Kasner's 9- (or 8-) year-old nephew (unnamed in the book's account of the event), when asked for a name for an enormous number. Perhaps influenced by comic strip character Barney Google. Googolplex coined at the same time, in the same way. Online Etymology Dictionary, © 2010 Douglas Harper How Many Is a Googol? | Wonderopolis Wonder of the Day #411 How Many Is a Googol? How many is a googol? What is an exponent? Is google a noun or a verb? Tags: Listen What's the biggest number you can think of? A million? A billion? A trillion? A gazillion? Infinity ? Long ago, mathematicians came up with an easy way of representing very large numbers. They created exponents (also called powers) to represent the mathematical function of multiplying a number by itself a certain number of times. Let's look at some examples. If you see 102, 10 is the base and the 2 is the exponent or power . 102 means 10 to the second power or 10 multiplied by itself twice.

Thus, 102 is the same as 10 X 10 or 100. Likewise, 103 is the same as 10 x 10 x 10, which equals 1,000. Do you see a pattern ? When 10 is the base , the exponent will be the number of zeroes after the 1 in the answer. So, 106 would be a 1 with 6 zeroes, or 1,000,000 (1 million). Exponents work with any base . For example, 42 is the same as 4 x 4 (16) and 43 is the same as 4 x 4 x 4 (64). How would 1 billion and 1 trillion be represented as exponents? One billion is 1 followed by 9 zeroes, or 109. One trillion is 1 followed by 12 zeroes, or 1012. Believe it or not, mathematicians use numbers much bigger than 1 trillion.

In 1938, a 9-year-old boy named Milton Sirotta, who was the nephew of American mathematician Edward Kasner, invented a new number that he called a googol . According to Milton, a googol is 10100, or 1 followed by 100 zeroes! How big is a googol ? Really, really big! Mathematicians believe a googol is bigger than the number of subatomic particles in the universe. Despite its size, a googol is still smaller than the total number of possible different games of chess (approximately 10120). Not content with the mind-blowing size of the googol , Milton also invented an even bigger number: the googolplex . A googolplex is 10 googol , or 1 with a googol of zeroes after it. How big is a googolplex ? If all the matter in the universe was turned into paper, it still wouldn't be enough paper to write down all the zeroes in a googolplex .

Even if you tried to write out all the zeroes in a googolplex — and could write two numbers per second — it would take you longer than the age of the universe to write it down! Googol and googolplex aren't used very often, except to show the difference between an incredibly large number and infinity …or to remind students how exponents can be used to generate huge numbers quickly. These terms did inspire one of the most famous and successful companies in the world today, though. Technology giant Google chose its name based upon a purposeful misspelling of googol . The company wanted to convey that its Internet search engine could provide huge quantities of information for its users. Google 's current headquarters in Mountain View, California, has come to be known as the Googleplex. Google now processes over 1 billion search requests every day. The main Google search engine is the Internet 's most-visited website. The Google search engine — a noun — has become so associated with Internet searching that google — a verb — was added to the dictionary. It means "to use the Google search engine to obtain information on the Internet." Wonder Words (14) Test your knowledge Wonder What's Next?

Set your sights on tomorrow’s Wonder of the Day if you’re interested in seeing in an all-new way! Try It Out Did the numbers in today's Wonder of the Day blow your mind? Dive deeper into big numbers with one or more of the following activities you can try with a friend or family member: What could you count that might require numbers as big as a googol? Have fun brainstorming things that exist in massive numbers. For example, such large numbers might come in handy if you were to try to count all the grains of sand on every beach in the world. What other ideas can you come up with? Be as creative as you can! Ask your friends and family members to help you with ideas. Ready to google? If you've never used the Google search engine before, give it a whirl. Type in your name, for example. What results does the search engine give you? Are any of them about you? Can you find information about someone who shares your name? Or you could type in a question you've always WONDERed about. How quickly can you find the answer using Google? There's much more to Google than just its search engine, though. Try one of these other fun features and see what you can learn!

Googolplex | Googology Wiki | Fandom powered by Wikia \(g_{\omega^{\omega^{\omega^2}}}(10)\) (exact) In popular culture Edit The company Google named their Mountain View headquarters "The Googleplex." [6] Even though googolplex is easily surpassed by larger numbers, it has nonetheless been used as a benchmark for a large quantity that is difficult to comprehend. In the documentary Cosmos: A Personal Voyage , Carl Sagan discusses the difficulty of writing out a googolplex. [7] Numbers near googolplex Edit Dario Alpern maintains a website listing the known factors of \(10^{10^{100}} + n\), [8] where n is an integer from 0 to 999. The case \(n = 1\) has the smallest known factor 316,912,650,057,057,350,374,175,801,344,000,001 (about 3.17*1035), found by Robert Harley. Several larger prime factors are known.

\(10^{10^{100}} + 37\) is the smallest with no known prime factors. A few of those numbers have a huge number of known factors due to their algebraic properties. In particular, \(10^{10^{100}} + 10\) has 57445 known prime factors, [9] beginning with: 2, 5, 7, 11 (appearing twice in factorization), 13, 19, 23, 503, 607, 739, 809, ... See also 3.2.1 - Large Numbers Large Numbers Plexing & The Googol Series 1 followed by ... When trying to come up with a really large number the first instinct is usually to write 1 followed by a lot of zeroes, or to define a number as 1 followed by a lot of zeroes. This is precisely what we are going to do now. Only we are not simply going to define some large number. Rather we're going to define the process.

Basically we want a function that takes "n" as input, where n is a natural number (counting number), and returns 1 followed by "n" zeroes as output. We will call this, for lack of a better name, the "plexing function". We now define: plex(n) = 1000000000 ... ... ... ... ... ... ... ... 00000000 with "n" zeroes We can write this more succinctly using exponential notation: plex(n) = 10^n We now have a simple but powerful tool to generate some very large numbers.

The Googol Using our new function we now define the "Googol" in the following way: Googol = plex(100) = 10^100 = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000 A Googol is 1 followed by a hundred zeroes. In the illion system A googol can also be named "ten duotrigintillion" in the short scale or "ten sexdecilliard" in the long scale. The story about how this number got coined tends to go something along these lines.

Sometime around the 1920s or 30s, depending on the account, the American mathematician Edward Kasner was trying to come up with a name for 1 followed by a hundred zeroes in order to interest children in the wonders of mathematics. On a walk with his nephews he asked them for suggestions. Nine year old Milton Sirotta suggested calling it a "googol". Amazingly the name has stuck and become universally recognized, even garnering enough acceptance to make it into the english dictionary. To give us some sense of perspective on the size of a googol, the sun contains only about 10^57 sub-atomic particles. How many sun's would we need to have a googol particles? To find out we simply divide a googol by 10^57 right? So we obtain: (10^100)/(10^57) = 10^(100-57) = 10^43 It would take 10^43 suns! Still not impressed? Well consider this. That means we would need about ten million trillion trillion trillion suns! There aren't even that many stars in the observable universe!

There are only about 10^80 sub-atomic particles in the observable universe. That means we would need about a hundred million trillion observable universes to have a googol particles. Pretty insane. Another way we could think about it would be to ask how much volume a googol particles would actually take up. Recall that most of the cosmos is empty space. What if we were to condense matter to the point where particles were pressing up against each other. 10^-18 meters is sometimes given as the diameter of a proton. Let's assume that every sub-atomic particle has about this radius. How large would a sphere packed solid with a googol sub-atomic particles be? To find out we can use the formula for the volume of a sphere and solve for the radius. We can say V = (4/3)pi*r^3 The volume will be equal to (10^100)*(10^-18m)^3 since we have a googol subatomic particles.

Let's see what we can obtain for the radius: (10^100)*(10^-18)^3 = (4/3)pi*r^3 10^100 * 10^-54 = (4/3)pi*r^3 10^46 = (4/3)pi*r^3 r^3 = (3/4)pi*10^46 r ~ 2.8668 x 10^15 Incredibly this sphere would have to be about 5.6 quadrillion meters across! That would be about a half a light year in diameter. That is WAY bigger than the entire solar system. It would be about 300 million trillion times the volume of our sun. That's a lot of particles! The Googolgong Interestingly, as a kid I never knew about the googol. For me the largest numbers I knew about were the centillion, which was 1 followed by 303 zeroes, and the unfathomable "googolgong". As I remember it me and my friend were being picked up by her father after elementary school.

I must have been talking about large numbers, because I had recently got interested in the subject for the first time. Her father than mentioned something about a number scientists had defined called a "googolgong". He said it was something like 1 followed by a hundred thousand zeroes. My mind was blown away trying to contemplate the "googolgong". This was probably an important impetus for the project that soon followed: An attempt to go way beyond the googolgong in an attempt to reach the infinite. What is particularly funny in retrospect is that the number a "googolgong" was entirely an invention of misinformation. To the best of my knowledge there had never been such a number as a googolgong until he had spoken of it. Obviously he must of heard about the googolplex (which we will get to next). Not only did he say the name incorrectly but he botched up the definition too! Its also interesting to note that it is significantly smaller than a googolplex, which just goes to show how ordinary people often fail to catch the full import of a large number definition. This being said however, the hearing of that number has forever left an impression on me.

It sounded off a gong in my head that rung seemingly without end for quite a while after. After "learning" of the googolgong I was hooked on the subject of large numbers, and that fascination has continued to this day. If scientists had come up with the googolgong (another erroneous and riddiculous detail) then I could best the scientists by coming up with even more tremendous numbers. But before we get ahead of ourselves lets try to come to terms with the "googolgong". Firstly we formally define it as: Googolgong = plex(100,000) = 10^100,000 This number is NOT merely a thousand times a googol. Rather it's a googol raised to the power of a thousand! That's a Googol googol googol googol googol ... ... ... ... ... ... googol googol googol where you have to say a googol a thousand times.

This is easy enough to prove: googol^1000 = (10^100)^1000 = 10^(100*1000) = 10^100,000 So what does this mean in terms of scale? Are we going to need at least a googol observable universes to have enough particles? Nope, it's much much worse. You see, if an observable universe (also known as a hubble volume) only contains 10^80 particles, then having a googol of them would only amount to: 10^80 * 10^100 = 10^(80+100) = 10^180 10^180 particles. Not even close. To reach a googolgong particles we are going to need a much more radical description. To reach a googolgong particles envision this: Imagine a hubble volume, floating in a vast sea of infinite darkness. Now imagine it shrinking down to the size of a sub-atomic particle as we zoom out to larger and larger scales.

Imagine also that there are many hubble volumes floating around in the local space, and as we zoom out there are more and more of them. Now imagine a truly vast space in which there are as many hubble volumes as there are particles within a hubble volume. That is, we can imagine we have 10^80 hubble volumes floating around. You can even imagine that this is just another universe in which each particle is itself a universe of our scale! Yikes! But that is only 10^160 particles so far. Now imagine that this "2nd order hubble volume" is just a merely sub-atomic particle in a third order hubble volume! Now we can imagine a 4th, 5th, 6th, 7th, 8th order hubble volume, and so on. How many orders would we have to go to reach a Googolgong particles? Well the 1,250th order hubble volume would contain roughly a Googolgong particles! Now go back to what we said a googol particles would be. We would need about a hundred million trillion hubble volumes.

However this would only be a tiny part of a 2nd order hubble volume. Yet you would have to go out to 1250 orders to reach a googolgong. A googolgong is not a couple billions or trillion times larger than a googol. It is completely in another league. If you haven't considered these ideas before they can get pretty dizzying. This however is pretty much business as usual in the world of large numbers, and we've only just begun. Next we will consider the googolplex! The Googolplex According to some tellings of the "googol and googolplex" story, it was milton sirotta who also coined a googolplex and defined it as 1 followed by as many zeroes as you can write before getting tired. Edward Kasner being a mathematician however would never settle for such an inpercise definition, yet he must have found the possibility of a number still larger than a googol intriguing. He therefore decided to have a googolplex defined as 1 followed by the largest number he had come up with, which was a googol of coarse. Some tellings also say that Kasner had come up with a googolplex as an afterthought.

Whatever the case may be a googolplex has also established itself and found its way into dictionaries. We can therefore define the googolplex as follows: Googolplex = plex(googol) = plex(10^100) = 10^(10^100) Perhaps you see now why I chose to call this a "plexing" function. We can use the -plex as a root that when added to a number generates 1 followed by that many zeroes. Thus a googol-plex is by definition 1 followed by a googol zeroes. A lot of impressive things have been said about a googolplex, and they are all more or less true, with no exaggeration neccessary. Here are some of the more popular illustrations of its size. Perhaps the most common thing said about the googolplex is that you could NEVER write it out fully in decimal notation no matter how hard you tried. That in itself is a little hard to grasp at first. Surely its a simple matter to write it out in decimal. Afterall we can write a googol in decimal right? Yes, but can you write out a googol of anything, let alone a googol zeroes?

That's the point. Even in decimal notation it would contain an exponential number of symbols so that it would be quite literally unwrittable. Perhaps your still not convinced. Heres the part where some number crunching is usually carried out to bring the point home. Well here it goes: Let's just say for argument sake that you can confidently write out about two zeroes every second. Okay. That means in one minute you can write out about 120 zeroes. Not a bad start. In an hour you could theoretically write out 7200 zeroes. Better. Of coarse your not likely to be able to keep up that pace and we still have a LONG LONG way to go. In a day of none stop writing you could perhaps get out anywhere from 86,400 to 172,800 zeroes depending on how well you can keep it up. I doubt even 80,000 would be possible because your wrist would probably want to fall off after just a few hours, but were just saying for arguments sake. Even after a day you still would have made only an infinitesimal fraction of progress, but lets continue anyway. Nobody ever accomplished anything by being a quiter right?

So perhaps you set aside an entire week to write out the googolplex once and for all and show the world that it is possible. Well you'd be lucky to get close to 600,000 zeroes, and that's assuming you average about 1 zero per second. That's without time for sleeping or eating, not to mention the amount of paper and ink you would need. Let's be a little more realistic. Even under the best circumstances your going to need at least, say, 4 hours of sleep each day, and at least an hour each day for eating. It's also not likely that a human can sustain 19 hours of writing at such a feverish pace. Let's say you need to take about a half hour break for every hour of writing. That means an average of about 1 zero per second during your working time. At this rate you might be able to get up to 480,000 zeroes. Even this is a rather extreme quota for a week however and perhaps beyond human endurance. So to be on the safe side let's say a person might get up to a 100,000 by their first week. Great!

Certainly impressive, but is a 100,000 really significant compared to a googol. No, not at all. hmm. So perhaps at least a year would be needed? Well a year is only about 52 weeks, so in theory a person could only write about 5,000,000 zeroes in that time. Millions of zeroes. That means that one could certainly write out a googolgong with enough money, patience, time, etc. But that's still a freaking drop in the bucket compare to writing out a googolplex. In fact even if a person lived to be a hundred an wrote out 10 million zeroes per year, he/she would only manage to get to about a billion zeroes. A billion is only 10^9, and this is no where close to a googol. Perhaps if enough people worked on it, it would be possible? Well even if we had everyone in the world (about 6.8 billion people) writing zeroes for a lifetime we still would only get about a million trillion zeroes, or 10^18 zeroes. This barely scratches the surface.

This is of coarse ignoring the fact that you would need enough paper and ink to write out those 10^18 zeroes. Okay, perhaps we couldn't write it out within our lifetime, but how long would it take to write out a googol zeroes? That's a valid question. Well let's just say for argument sake that instead of writing it out you got a printer to print it out. Let's say it can print a line of 50 zeroes about every 2 seconds. How long would it take to print out a googolplex? A hopelessly long time of about 10^91 years. What?! That's barely smaller than a googol itself! Well actually it's about a billionth of a googol, but I know what you mean. This time scale is so long that the universe would have to be about 10^81 times its current age in order for the printer to have enough time. Hopefully your are now fully convinced of the futility of trying to write out a googolplex in decimal notation. But there is also a much more basic reason why writing out a googolplex is clearly impossible, besides the amount of man hours it would require.

We wouldn't even be able to stuff all of the stacks of paper that a googolplex would be written out on into the observable universe! That may seem totally incredible, but it pays to recall that there are only 10^80 sub-atomic particles in the observable universe. You might recall however that most of the universe is empty space, and we were able to compact a googol particles into a sphere with a diameter of about half a light year. Couldn't we somehow fit a googol zeroes in the observable universe then? Well here is some number crunching for the skeptics. Firstly we need to find the volume of the observable universe. A good way to come up with an estimate is to let the radius of it be as many light years as the age of the universe. Currently the age is estimated at about 13,000,000,000 years. The speed of light is about 300 million meters per second.

Combining this all into the formula for the volume of a sphere we obtain: (4/3)pi*(3e8*60*60*24*365*1.3e10)^3 ~ (4/3)pi*(1.23e26)^3 ~ 7.79 x 10^78 m^3 So the volume of the observable universe is about 7.79x10^78 cubic meters. So how much space would a single zero take up. Well it depends how large or small its written, but we can assume that a zero can be written on a half centimeter square without much trouble. Paper can be as thin as about a tenth of a milimeter. Multiplying these dimensions in meters we obtain: (0.005m)(0.005m)(0.0001m) = 0.0000000025 m^3 That's incredibly small. Yet when we divide the volume of the universe by the minimal volume required for each zero we obtain only about 10^87.

That means we can't stuff more than about 10^87 digits into the universe. Maybe 10^88 if we write it really small on really thin paper, but that's it. We aren't going to make it to a googol. If we can't even write out a googolplex, what possible hope to we have of imagining the size of the number itself! Well remember how we described multiple levels of hubble volumes within hubble volumes like a series of babushka dolls to explain the size of a googolgong.

Well to reach a googolplex particles we would not go to the 1,250th order hubble volume, but would have to ascend to a maddeningly high 125,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000th order hubble volume. That's 1.25x10^98 orders! That is the truly insane magnitudes we are talking about. I doubt you've heard the googolplex described in this way before, but I think this really brings out the other worldliness of these numbers. The Googol Series: The Googolplexian and Beyond...

The googolplex is often cited as the "largest named number" because it is universally recognized. This is a somewhat questionable claim on account of many other numbers with well established names, such as skewe's number, and graham's number to name a few. Also a googolplex is really just the very beginning of the large numbers game. Consider this, if we can have 1 followed by a googol zeroes, why not 1 followed by a googolplex zeroes! Now we'd need to go up to the googolth order hubble space just to have enough space to write out the damn thing, let alone have that many particles! Some names have been suggested for this number, such as the "googolplexian", a "gargoogolplex", or the "googolplexplex", but none of these work very well in my opinion. There does seem to be some concensus that a "googolduplex" is probably the best choice. This is the term that Jonathan Bowers, myself, and many others use. Essentially its a shortening of "googolplexplex" by using the latin prefix for two.

Notice how we can define a googolduplex: Googolduplex = plex(googolplex) = plex(plex(googol)) = plex(plex(10^100)) = plex(10^(10^100)) = 10^(10^(10^100))

Question: The number equating to 1 followed by 100 zeroes is known as a what?
Answer: GOOGOL