googol

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

A googol is the large number 10¹⁰⁰, that is, the digit 1 followed by one hundred zeroes. 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 googol 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 googol 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 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

Relation to -illion number names

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

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<math>\times</math>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

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

• A little googol is 2^100 ~= 1.267*10^30 and a little googolplex is 2^(2^100) ~= 10^(3.8*10^29).

• 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. Lawrence E. Page: "Lucas Pereira: 'You idiots, you spelled "Googol" wrong!' But this was good, because google.com was available and googol.com was not. Now most people spell 'Googol' 'Google', so it worked out OK in the end."

Googolplex

A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol: <math>{10}^\mbox{googol}</math> = <math>\,\!{10}^{{10}^{100}}</math>.

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'
• googol.com
• "There Could Be No Google Without Edward Kasner", Carl Bialik, The Wall Street Journal Online, June 14, 2004.