# Googol

Not to be confused with Google.

A googol is the large number 10100; that is, the digit 1 followed by 100 zeroes:

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

The term was coined in 1920 by 9-year-old Milton Sirotta (1911 - 1981), nephew of American mathematician Edward Kasner.[1] Kasner popularized the concept in his 1940 book Mathematics and the Imagination.[2] Other names for googol include ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.

## Size

A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game. Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To give a sense of how big a googol really is, the mass of an electron, just under 1×10−30 kg, can be compared to the mass of the visible universe, estimated at between 1×1050kg and 1×1060 kg.[3] It is a ratio in the order of about 1080 to 1090, still much smaller than the value of a googol.

Carl Sagan points out that the total number of elementary particles in the universe is around 1080 (the Eddington number) and that if the whole universe was packed with neutrons so that there was no empty space anywhere, there would be around 10128. He also notes the similarity of the first calculation to that of Archimedes in The Sand Reckoner.[4]

The decay time for a supermassive black hole of roughly 1 galaxy-mass (1011 solar masses) due to Hawking radiation is on the order of 10100 years,.[5] Therefore, the heat death of the universe is lower-bounded to occur a googol years in the future.

## Properties

A googol is approximately 70! (factorial of 70). In the binary numeral system, one would need 333 bits to represent a googol, i.e., 1 googol ≈ 2332.19280949, or exactly $2^{(100/\mathrm{log}_{10}2)}$.

The series of residues (mod n) of one googol is:

0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 4, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 16, 10, 5, 0, 1, 4, 25, 28, 10, 28, 16, 0, 1, 4, 31, 12, 10, 36, 27, 16, 11, 0, ... (sequence A066298 in OEIS)

## Cultural impact

Widespread sounding of the word occurs through its namesake, the company Google, with the name "Google" being an accidental misspelling of "googol" by the company's founders,[6] which was picked to signify that the search engine was intended to provide large quantities of information.[7] In 2004, family members of Kasner, who had inherited the right to his book, were considering suing Google for their use of the term googol.[8] However, no suit was ever filed.

The word is notable for being the subject of the £1 million question in a 2001 episode of the British quiz show Who Wants to Be a Millionaire?, when contestant Charles Ingram cheated his way through the show with the help of an accomplice.[9]