A googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). In Mathematics and Computer science, a digit is a symbol (a number symbol e The decimal ( base ten or occasionally denary) Numeral system has ten as its base. The term was coined in 1938[1] by Hardik Upadhyay (1886–1980), nephew of Bharatiya mathematician Pingala. A mathematician is a person whose primary area of study and research is the field of Mathematics. Pingala ( पिङ्गल piṅgalá) was an ancient Indian writer famous for his work the Chandas Shastra ( chandaḥ-śāstra Kasner popularized the concept in his book Mathematics and the Imagination (1940).
Googol is of the same order of magnitude as the factorial of 70 (70! being approximately 1. 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 Definition The factorial function is formally defined by n!=\prod_{k=1}^n k 198 googol, or 10 to the power 100. 0784), and its only prime factors are 2 and 5 (100 of each). In Number theory, the prime factors of a positive Integer are the Prime numbers that divide into that integer exactly without leaving a remainder In binary it would take up 333 bits. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication A googol has no particular significance in mathematics, but is useful when comparing with other incredibly large quantities such as the number of subatomic particles in the visible universe or the number of possible chess games. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Chess is a recreational and competitive Game played between two players. Edward Kasner created it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. Edward Kasner (1878&ndash1955 ( City College of New York 1897 Columbia University M In Mathematics, the affinely extended real number system is obtained from the Real number system R by adding two elements +∞ and &minus∞ (pronounced
A googol can be written in conventional notation as follows:
- 1 googol
- = 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
Its official English number name is ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale. Names of numbers larger than a quadrillion are almost never used for reasons discussed further below The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French Names of numbers larger than a quadrillion are almost never used for reasons discussed further below
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Googolplex
A googolplex is the number one followed by one googol zeroes, or ten raised to the power of one googol:
- 10googol = 10(10100).
In the documentary Cosmos, physicist and broadcast personality Carl Sagan estimated that writing a googolplex in numerals (i. Cosmos A Personal Voyage is a thirteen-part television series written by Carl Sagan, Ann Druyan, and Steven Soter, with Sagan Carl Edward Sagan ( November 9 1934 &ndash December 20 1996) was an American Astronomer, astrochemist, author e. , "1,000,000,000. . . ") would be physically impossible, since doing so would require more space than the known universe occupies.
Googol and comparable large numbers
A googol is greater than the number of atoms in the observable universe, which has been variously estimated from 1079 up to 1081 [2][3]. In Big Bang Cosmology, the observable universe is the region of space bounded by a Sphere, centered on the observer that is small enough that Less than a googol Planck times have elapsed since the Big Bang (the current figure stands at around 8×1060 Planck times). In Physics, the Planck time ( tP) is the unit of Time in the system of Natural units known as Planck units. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. From the previous two figures, it can be seen that a list of where every particle is at every possible discernible unit of time since the Big Bang would contain over a googol entries, but still far less than a googolplex: around 8 × 10140. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation.
A little googol is 2100 (about 1. 268×1030), or 1,267,650,600,228,229,401,496,703,205,376, while a little googolplex is 
or about 
.
Avogadro's number, 6. The Avogadro constant (symbols L, N A also called Avogadro's number, is the number of "elementary entities" (usually Atoms 02214179×1023, is exactly the number of 12C atoms in 12 grams (0. Carbon ( C)Standard atomic mass 120107(8 u Natural isotopes See also Carbon-12, Carbon-13, Carbon-14 012 kg) of unbound 12C in its ground state. It is perhaps the most widely known large number from chemistry and physics. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Avogadro's number is less than the fourth root of a googol.
Black holes are presumed to evaporate because they faintly give off Hawking radiation; if so, a supermassive black hole would take about a googol years to evaporate. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Hawking radiation (also known as Bekenstein-Hawking radiation) is a Thermal radiation with a black body spectrum predicted to be emitted by Black holes A supermassive black hole is a Black hole with a Mass of an order of magnitude between 105 and 1 [4]
Seventy factorial, or 70!, is "just 1. Definition The factorial function is formally defined by n!=\prod_{k=1}^n k 19785717 × 10100. This means that there are over a googol ways to arrange seventy items (or people) in a sequence (such as a line to a concert). A concert is a live Performance, usually of Music, before an Audience.
The Shannon number, 10120, a rough lower bound on the number of possible chess games, is more than a googol. The Shannon number, 10120 is an estimated lower bound on the Game-tree complexity of Chess, calculated by information theorist
A googol is considerably less than the number described in the ancient Archimedes' story of The Sand Reckoner, namely 
But it should be noted that the system invented by Archimedes is reminiscent of a positional numeral system with base 108, so that Archimedes' number could be written ![\left[\left((10)^{(10)}\right)^{10}\right]_{10^8}=\left[10^{100}\right]_{10^8}](../../../../math/1/8/9/189dc9a2ce4882ca54fc4031450d30ee.png)
, that is, one googol in base 108
On a practical level, googol is perhaps the most worthless number in existence (next to the Shannon number). Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer The Sand Reckoner ( Greek: Ψαμμίτης Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer The Shannon number, 10120 is an estimated lower bound on the Game-tree complexity of Chess, calculated by information theorist
In popular culture
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 allegedly attempted to defraud the quiz show on 10 September 2001. The Pound Sterling ( symbol £; ISO code: GBP) subdivided into 100 pence (singular penny) is the Currency In the United Kingdom, Who Wants to Be a Millionaire? is a Television Quiz show which offers a maximum Cash prize of one million Charles Ingram (born 6 August 1963) is a former British Army major and Novelist who made headlines in the United Kingdom Events 506 - The Bishops of Visigothic Gaul meet in the Council of Agde. Year 2001 ( MMI) was a Common year starting on Monday according to the Gregorian calendar. The other options were a megatron, a gigabit or a nanomole. A gigabit is a unit of information or computer storage abbreviated Gbit (or Gb) [5]
Googol is one of the 336 vocabulary words in the board game Balderdash, and their definition on the back of the card is "The number one followed by 100 zeros. "
In the January 23, 1963 Peanuts strip, Lucy asks Schroeder what the chances are of them getting married, and Schroeder responds "Oh, I'd say about 'googol' to one. Events 393 - Roman Emperor Theodosius I proclaims his nine year old son Honorius co-emperor Year 1963 ( MCMLXIII) was a Common year starting on Tuesday (link will display full calendar of the Gregorian calendar. Peanuts is a syndicated daily and Sunday Comic strip written and illustrated by Charles M "
In an episode of the animated series Teenage Mutant Ninja Turtles: Fast Forward, the "Gaminator" video games system is said to have a "3-googolhertz processor. Teenage Mutant Ninja Turtles is an American animated series, mainly set in New York City. "
"A googol is precisely as far from infinity as is the number one. " — Carl Sagan, Cosmos
The company name Google is a misspelling of the word "Googol" made by founders Larry Page and Sergey Brin, as described in the book The Google Story by David A. Vise. Carl Edward Sagan ( November 9 1934 &ndash December 20 1996) was an American Astronomer, astrochemist, author Cosmos A Personal Voyage is a thirteen-part television series written by Carl Sagan, Ann Druyan, and Steven Soter, with Sagan Google Inc is an American public corporation, earning revenue from advertising related to its Internet search, e-mail, online David A Vise is a journalist and writer He won a Pulitzer Prize in 1990 while working as a business reporter for the Washington Post.
See also
References
- ^ Kasner, Edward and James Newman, Mathematics and the Imagination, 1940, Simon and Schuster, New York. Names of numbers larger than a quadrillion are almost never used for reasons discussed further below Year 1940 ( MCMXL) was a Leap year starting on Monday (link will display the full 1940 calendar of the Gregorian calendar. ISBN 0-486-41703-4
- ^ Estimate of the number of atoms in the Universe; 1078 up to 1081
- ^ Another estimate of the number of atoms in the Universe; 4 × 1079
- ^ On the dark side, p. 4
- ^ Millionaire's route to the top prize
External links
- History from the Google website
- Eric W. Weisstein, Googol at MathWorld. Eric W Weisstein (born March 18, 1969, in Bloomington Indiana) is an Encyclopedist who created and maintains MathWorld MathWorld is an online Mathematics reference work created and largely written by Eric W
- googol at PlanetMath. PlanetMath is a free, collaborative online Mathematics Encyclopedia.
- "Tridecabillion" by Paul Niquette
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