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Googol

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A googol is the large number 10, that is, the digit 1 followed by one hundred zeros (in decimal representation). One way of grasping its size is that it is equivalent to multiplying the product of 1 million by 1 million 15 times, then further multiplying that by ten thousand. The term was coined in 1920 by nine-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination.

A googol is of the same order of magnitude as the factorial of 70 (70! being approximately 1.198 googols, 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.

The 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. 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.

Writing out a googol

A googol can be written in conventional notation as follows:

1 googol = 10 =
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 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 {\displaystyle \scriptscriptstyle 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}

The shrinking googol

Back when it was named in 1938, the googol was undeniably large. However, with the invention of fast computers and fast algorithms, computation with numbers the size of a googol has become routine. For example, even the difficult problem of prime factorization is now fairly accessible for 100-digit numbers.

The largest number that can be represented by a typical pocket calculator for high school or scientific use is slightly less than a googol (e.g. 9.9999999 E+99, i.e. 9.9999999×10, or 0.99999999 googol). However, some models allow exponents larger than 99.

Googolplex

Main article: googolplex

A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol:

googolplex = 10 googol = 10 ( 10 100 ) . {\displaystyle {\mbox{googolplex}}={10}^{\mbox{googol}}={10}^{({10}^{100})}.}

Trivia

  • Avogadro's number, 6.022x10, can loosely be thought of as the number of hydrogen atoms in a gram of hydrogen gas, and is perhaps the most widely known large number from chemistry and physics. Avogadro's number is much less than a googol.
  • A little googol is 2, or about 1.267x10
  • A googol is greater than the number of particles in the known universe, which has been variously estimated from 10 up to 10.
  • 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.
  • If seventy people were lining up to enter a concert, how many different ways could they be arranged? Quite a few, 1.19785717 × 10 to be precise, or seventy factorial.
  • The Shannon number is a rough estimate of the number of possible chess games, and it is more than a googol, around the order of 10.
  • A googol is considerably less than the number described in the ancient Greek story of The Sand Reckoner, namely 10 8 × 10 16 {\displaystyle 10^{8\times 10^{16}}} .
  • A little googolplex is 2 2 100 {\displaystyle 2^{2^{100}}} or about 10 3.8 × 10 29 {\displaystyle 10^{3.8\times 10^{29}}} .
  • "A googol is precisely as far from infinity as is the number one." - Carl Sagan, Cosmos
  • Googol was the answer to the million-pound question on Who Wants to Be a Millionaire? when Major Charles Ingram allegedly defrauded the quiz show on 10 September 2001.
  • The Internet search engine Google was named after this number. The original founders were going for 'Googol', but ended up with 'Google' due to a spelling mistake on a cheque that investors wrote to the founders.
  • In one Peanuts strip, Lucy asks Schroeder what the chances are of them getting married, and Shroeder responds "about a googol to one."

See also

References

External link

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