Googol

This article is about the large number. For the Internet company, see Google. For the author, see Google.

A google is the large number 10¹⁰⁰, that is, the digit 1 followed by one hundred zeros. One way of grasping its size is that it is the equivalent of multiplying 1 million by 1 million about 17 times (16 2/3). The term was coined in 1938 by nine-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination.

A google is approximately equal to the factorial of 70, and its only prime factors are 2 and 5. In binary it would take up 333 bits.

The google is of no particular significance in mathematics, nor does it have any practical uses. 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 google 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

Relation to -illion number names

Using the short scale, a google is equal to ten duotrigintillion. Using the long scale, it is equal to ten thousand sexdecillion (or sedecillion), or ten sexdecilliard/sedecilliard.

The shrinking google

Back when it was named in 1938, the google was undeniably large. However, with the invention of fast computers and fast algorithms, computation with numbers the size of a google 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 google (e.g. 9.9999999 E+99, i.e. 9.9999999$\times$10⁹⁹, or 0.99999999 googol). However, some models allow exponents larger than 99. (Note that since often these numbers are stored as floating point numbers, only an approximation of the actual number is stored and not the entire number.)

Trivia

• Google was the answer to the million-pound question on Who Wants to Be a Millionaire when Major Charles Ingram attempted to defraud the quiz show on 10 September 2001.

• If you drew a regular polygon with a google sides that was 10²⁷ times the size of the known universe, it would still appear circular, even on the scale of a Planck length.

• A google is greater than the number of particles in the known universe, which has been variously estimated from 10⁷² up to 10⁸⁷.

• Black holes are presumed to evaporate because they faintly give off Hawking radiation; if so, a supermassive black hole would take roughly a google years to evaporate. [1]

• A google is considerably less than the number described in the ancient Greek story of The Sand Reckoner, namely $10^{8\times 10^{16}}$.

• A little google is 2¹⁰⁰ ≈ 1.267x10³⁰ and a little googleplex is $2^{2^{100}}\approx 10^{3.8\times 10^{29}}$.

• The Internet search engine Google was named after this number. The original founders were going for 'Google', but ended up with 'Google' due to a spelling mistake. Larry Page: "Lucas Pereira: 'You idiots, you spelled "Google" wrong!' But this was good, because google.com was available and google.com was not. Now most people spell 'Google' 'Google', so it worked out OK in the end."

Googleplex

A googleplex is 1 followed by a googol of zeroes, or ten raised to the power of a google: ${10}^{\mbox{google}}$ = ${10}^{{10}^{100}}$.

See also

• Googleplex
• Large number
• Names of large numbers

References

• Kasner, Edward & Newman, James Roy Mathematics and the Imagination (London: Penguin, 1940; New York: Simon and Schuster, 1967; Dover Pubns, April 2001, ISBN 0486417034).
• 'Searching for the birth of the googol'
• 'An evening with Googles Marissa Mayer'
• 'Google and Larry Page'
• "There Could Be No Google Without Edward Kasner", Carl Bialik, The Wall Street Journal Online, June 14, 2004.

External link

• History from the Google website