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Thursday, 6 November 2008

Math: What is a Googol?

A googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). The term was coined in 1938 by Milton Sirotta. Kasner popularized the concept in his book Mathematics and the Imagination (1940).

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
Its official English number name is ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.

Googolplex

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

10googol = 10(10100).

Googol and comparable large numbers

A googol is greater than the number of atoms in the observable universe, which has been variously estimated from 1079 up to 1081.

Less than a googol Planck times have elapsed since the Big Bang (the current figure stands at around 8×1060 Planck times). Similarly, the size of the observable universe is about 9×10185 cubic Planck lengths. From the previous figures it can be seen that a list of positions of every particle at every possible instant of time, at the maximum possible accuracy, would contain well over a googol entries (of the order of 10325), but still far less than a googolplex. Avogadro's number, 6.02214179×1023, is exactly the number of 12C atoms in 12 grams (0.012 kg) of unbound 12C in its ground state.

It is perhaps the most widely known large number from chemistry and physics.

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 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.

Source: Wikipedia

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I am a grade nine student living in Mexico. This is my home school education blog. I post the things I learned during the week on this blog. I hope you can learn things from this too.


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