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Template:Two other uses Googol is the large number 10¹⁰⁰, that is, the digit 1 followed by one hundred zeros (in decimal representation). The term was coined in 1920 by nine-year-old Milton Sirotta (1911–1981), nephew of American mathematician Edward Kasner. 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 1.198 googol, or 10 to the power 100.0784), and its only prime factors are 2 and 5 (100 of each). In binary it would take up 333 bits.

Googol is of 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. 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.

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.

Googolplex

A googolplex is the number one followed by one googol zeroes, or ten raised to the power of one googol:

10^googol = 10^10¹⁰⁰.

In the documentary Cosmos, physicist and broadcast personality Carl Sagan estimated that writing a googolplex in numerals (i.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 elementary particles in the observable universe, which has been variously estimated from 10⁷⁹ up to 10⁸¹ ^[1]^[2]. Less than a googol Planck times have elapsed since the Big Bang (the current figure stands at around 8×10⁶⁰ Planck times). From the previous two figures, it can be seen that a list of where every particle is at every possible discernable unit of time since the Big Bang would contain over a googol entries, but still far less than a googolplex: around 8 × 10¹⁴⁰.

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 $2^{2^{100}}$ or about $10^{3.8\times 10^{29}}$ .

Avogadro's number, 6.02214179 × 10²³, is exactly the number of ¹²C atoms in 12 grams (0.012 kg) of unbound ¹²C in its ground state. It is perhaps the most widely known large number from chemistry and physics. 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.^[3]

Seventy factorial, or 70!, is "just over" a googol: 1.19785717 × 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).

The Shannon number, 10¹²⁰, a rough lower bound on the number of possible chess games, is more than a googol.

A googol is considerably less than the number described in the ancient Archimedes' story of The Sand Reckoner, namely $\left((10^{8})^{(10^{8})}\right)^{(10^{8})}=10^{8\cdot 10^{16}}.$ 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 $\left[\left((10)^{(10)}\right)^{10}\right]_{10^{8}}=\left[10^{100}\right]_{10^{8}}$ , that is, one googol in base 10⁸

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 other options were a megatron, a gigabit or a nanomol.^[4]

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."

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."

"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.

References

^ Estimate of the number of particles in the Universe; 10⁷⁹ up to 10⁸¹
^ Another estimate of the number of particles 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
Weisstein, Eric W. "Googol". MathWorld.
googol at PlanetMath.
"Tridecabillion" by Paul Niquette

[1] Estimate of the number of particles in the Universe; 10⁷⁹ up to 10⁸¹

[2] Another estimate of the number of particles in the Universe; 4 × 10⁷⁹

[3] On the dark side, p.4

[4] Millionaire's route to the top prize

[1]

[2]

[3]

[4]

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 {{two other uses||the Internet company|Google|the Russian author|Nikolai Gogol}}
-'''Googol''' is the [[large number]] 1.0<sup>100</sup>, that is, the [[numerical digit|digit]] 1 followed by one hundred [[0 (number)|zeros]] (in [[decimal]] representation).
+'''Googol''' is the [[large number]] 10<sup>100</sup>, that is, the [[numerical digit|digit]] 1 followed by one hundred [[0 (number)|zeros]] (in [[decimal]] representation).
 The term was coined in 1920 by nine-year-old Milton Sirotta (1911–1981), nephew of American [[mathematician]] [[Edward Kasner]]. Kasner popularized the concept in his book ''Mathematics and the Imagination'' (1940).