Googol

A googol is the large number 10¹⁰⁰, 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 16 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 = 10¹⁰⁰ =

\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

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. 9.9999999×10⁹⁹, or 0.99999999 googol). However, some models allow exponents larger than 99.

Trivia

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.
Avogadro's number, 6.022x10²³, 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 googol 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 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 × 10¹⁰⁰ 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 10¹²⁰.
A googol is considerably less than the number described in the ancient Greek story of The Sand Reckoner, namely $10^{8 \times 10^{16}}$ .
A little googol is 2¹⁰⁰ ≈ 1.267x10³⁰ and a little googolplex 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 'Googol', but ended up with 'Google' due to a spelling mistake on a check that investors wrote to the founders.

Googolplex

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

\mbox{googolplex} = {10}^{\mbox{googol}} = {10}^ .

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

Large numbers

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