A Googol is a known finite number. A Googillion is a larger unknown finite number.
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Not to be confused with Google, the Internet company,
Googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). The term was coined in 1920 by nine-year-old Milton Sirotta (1911–1981), nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination (1940).
Googol is of the same order of magnitude as the factorial of 70 (70! being approximately 1.198 googol, 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.
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.
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
A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol:
- 10googol = 1010100.
In the documentary Cosmos, physicist and broadcast personality Carl Sagan estimated that writing a googolplex in numerals (i.e., “1,000,000,000…”) would be physically impossible, since doing so would require more space than the known universe occupies.
Googol and comparable large numbers
- A googol is greater than the number of elementary particles in the observable universe, which has been variously estimated from 1079 up to 1081,.
- A little googol is 2100 (about 1.268×1030), or 1,267,650,600,228,229,401,496,703,205,376, while a little googolplex is or about .
- Avogadro’s number, 6.0221415×1023, can loosely be thought of as the number of carbon atoms in twelve grams of elemental carbon, and is perhaps the most widely known large number from chemistry and physics. Avogadro’s number is much less than a googol.
- 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.
- Seventy factorial, or 70!, is just over a googol, 1.19785717 × 10100. This means that there are over a googol ways to arrange seventy items (or people) in a sequence (such as a line to a concert).
- The Shannon number, 10120, a rough lower bound on the number of possible chess games, is more than a googol.
- A googol is considerably less than the number described in the ancient Archimedes‘ story of The Sand Reckoner, namely But it should be noted that the system invented by Archimedes is reminiscent of a positional numeral system with base 108, so that Archimedes‘ number could be written that is 1 googol in base 108; a remarkable coincidence indeed!
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