Agoogol is the large number10100. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 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 systematic nameis10 duotrigintillion (the short scale names are standard in the English-speaking world). Its prime factorization is
A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game. Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To put in perspective the size of a googol, the mass of an electron, just under 10−30kg, can be compared to the mass of the visible universe, estimated at between 1050 and 1060kg.[5] It is a ratio in the order of about 1080 to 1090, or at most one ten-billionth of a googol (0.00000001% of a googol).
Another way of illustrating the immense size of a googol is to picture the Frontier supercomputer, which as of 2022 is the most powerful supercomputer in the world and measures 680 m2 (7,300 sq ft), almost exactly the same size of a basketball court with run-offs and sidelines.[6] The Frontier is capable of making 1,102,000 TFLOPs (1.1 quintillion calculations per second). If the supercomputer was shrunk down to the size of an atom (for reference, a typical grain of sand might have 37 quintillion atoms),[7] and if every atom in the observable universe (~1080 atoms total[8]) was as powerful as a Frontier supercomputer, it would take approximately 100 seconds of parallel computing to manually add up all the digits [clarification needed] like an adding machine (instead of using shorthand calculations).[dubious – discuss]
Carl Sagan pointed out that the total number of elementary particles in the universe is around 1080 (the Eddington number) and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be around 10128. He also noted the similarity of the second calculation to that of ArchimedesinThe Sand Reckoner. By Archimedes's calculation, the universe of Aristarchus (roughly 2 light years in diameter), if fully packed with sand, would contain 1063 grains. If the much larger observable universe of today were filled with sand, it would still only equal 1095 grains. Another 100,000 observable universes filled with sand would be necessary to make a googol.[9]
A googol is approximately 70! (factorial of 70).[a] Using an integral, binary numeral system, one would need 333 bits to represent a googol, i.e., 1 googol = ≈ 2332.19280949. However, a googol is well within the maximum bounds of an IEEE 754double-precisionfloating point type, but without full precision in the mantissa.
Using modular arithmetic, the series of residues (mod n) of one googol, starting with mod 1, is as follows:
Widespread sounding of the word occurs through the name of the company Google, with the name "Google" being an accidental misspelling of "googol" by the company's founders,[12] which was picked to signify that the search engine was intended to provide large quantities of information.[13] In 2004, family members of Kasner, who had inherited the right to his book, were considering suing Google for their use of the term "googol";[14] however, no suit was ever filed.[15]
Since October 2009, Google has been assigning domain names to its servers under the domain "1e100.net", the scientific notation for 1 googol, in order to provide a single domain to identify servers across the Google network.[16][17]
^Kasner, Edward; Newman, James R. (1940). Mathematics and the Imagination. Simon and Schuster, New York. ISBN0-486-41703-4. Archived from the original on 2014-07-03. The relevant passage about the googol and googolplex, attributing both of these names to Kasner's nine-year-old nephew, is available in James R. Newman, ed. (2000) [1956]. The world of mathematics, volume 3. Mineola, New York: Dover Publications. pp. 2007–2010. ISBN978-0-486-41151-4.
^Sagan, Carl (1981). Cosmos. Book Club Associates. pp. 220–221.
^Page, Don N. (1976-01-15). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole". Physical Review D. 13 (2). American Physical Society (APS): 198–206. Bibcode:1976PhRvD..13..198P. doi:10.1103/physrevd.13.198. ISSN0556-2821. See in particular equation (27).
^Nowlan, Robert A. (2017). Masters of Mathematics: The Problems They Solved, Why These Are Important, and What You Should Know about Them. Rotterdam: Sense Publishers. p. 221. ISBN978-9463008938.