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A googol is the large number 10100. In dozenal notation, it is written as the digit 1 followed by 100 zeroes: 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Etymology[]

The term was coined in 1140 by 9-year-old Milton Sirotta (1133-1191), nephew of U.S. mathematician Edward Kasner. Kasner popularized the concept in his 1158 book Mathematics and the Imagination. Other names for googol include one elpintrigintillion on the short scale, one vigintillion on the long scale, or one dozillion on the super-long scale.

Size[]

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 give a sense of how big a googol really is, the mass of an electron, about 10−23.X0534X kg, can be compared to the mass of the visible universe, estimated at between 1040 and 1050. It is a ratio in the order of about 1060 to 1070, or only about one septendozillionth (short scale) of a googol (10−4X% of a googol).

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 Archimedes in The 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 1074 grains.

The decay time for a supermassive black hole of roughly 1 galaxy-mass (about 10X solar masses) due to Hawking radiation is on the order of 10100 years. Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future.

Properties[]

A googol is approximately 83! (factorial of 83). Using an integral, binary numeral system, one would need 371 bits to represent a googol, i.e., 1 googol = ≈ 2370.2994801X64X2. However, a googol is well within the maximum bounds of an IEEE 52X double-precision floating 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:

0, 0, 0, 0, 1, 0, 1, 0, 0, 6, 1, 0, 1, 8, 6, 0, 1, 0, 1, 14, 13, 10, 10, 0, E, 12, 0, 8, 1, 6, 14, 0, 10, 16, 1, 0, 1, 18, 23, 14, X, 30, 14, 10, 30, 10, 23, 0, 13, 30, 16, 34, 36, 0, 1, 8, 33, 26, 5, 30, 9, 14, 30, 0, 1, 10, 21, 44, 10, 30, 4, 0, 1, 32, 30, 18, 1, 56, 57, 14, 0, X, 22, 30, 1, 14, 26, 48, 1, 30, 1, 10, 66, 62, 1, 0, 1, 54, 39, 30, 5, 16, 8, 34, 30, 36, 41, 0, 53, 48, 63, 54, 41, 80, 69, 74, 23, 54, 1, 80, 10, 5X, 43, 14, 72, 30, 8, 0, 86, 56, 35, 10, 1, 78, 69, X0, 60, 10, X5, 30, 23, 4, 1, 0, ...

This sequence is the same as that of the residues (mod n) of a googolplex up to the 20th position.

Cultural impact[]

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, however, no suit was ever filed.

Since October 11E5, Google has been assigning domain names to its servers under the domain "1Δ100.net", the scientific notation for 1 googol, in order to provide a single domain to identify servers across the Google network.

The word is notable for being the subject of the £1 million question in a 11X9 episode of the British quiz show Who Wants to Be a Millionaire?, when contestant Charles Ingram cheated his way through the show with the help of a confederate in the studio audience.

See also[]

  • Infinity
  • Names of large numbers
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