A googol number can be shown by writing a “1” followed by one hundred “0”s: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
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A googol is a very large number, equivalent to ten to the power of one hundred. Dr. Edward Kasner, a notable American mathematician, first introduced the term ‘googol’ in his book ‘Mathematics and the Imagination’ in 1940. According to Dr. Kasner, “a googol is a 1 followed by one hundred zeros.” Thus, in numbers, a googol can be expressed as 10^100.
To show a googol number, one could write a “1” followed by one hundred “0”s, which would look like this:
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.
The importance of a googol is primarily in its sheer enormity. It is much larger than the number of particles in the observable universe, estimated to be around 10^80. The googol is a valuable concept in mathematics, probability theory, and physics.
Another important concept related to the googol is the googolplex. It is equal to ten to the power of a googol(10^googol), and it is such an immense number that it cannot be written out in full because it would require more space than is available in the universe!
In conclusion, a googol is an incredibly large number and is useful in various fields of science and mathematics. As Richard Feynman said, “What is remarkable about this is that once you get past a few thousand, the names of the numbers become quite arbitrary…who’s going to remember the name of a number like 133,542,010,000,531? People can remember the name ‘googol’.”
Here is a table to illustrate how a googol compares to other large numbers:
| Number | Value |
|---|---|
| Million | 1×10^6 |
| Billion | 1×10^9 |
| Trillion | 1×10^12 |
| Quadrillion | 1×10^15 |
| Quintillion | 1×10^18 |
| Sextillion | 1×10^21 |
| Septillion | 1×10^24 |
| Octillion | 1×10^27 |
| Nonillion | 1×10^30 |
| Decillion | 1×10^33 |
| Centillion | 1×10^303 |
| Googol | 1×10^100 |
| Googolplex | 10^googol |
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Numberphile discusses the enormous size of a googol, which is 1 followed by 100 zeros, larger than the number of particles in the universe. However, a googolplex, which is 10 raised to the power of a googol, is so large that it cannot be written down even if every particle in the universe were used for it. A person or object occupying a meter cubed of space would have roughly 10 to the power of 10 to the power of 70 possible states, much smaller than a googolplex. If the universe were googolplex meters across, there would be repeating volumes of one meter cubed and eventually, an entire observable universe would repeat, highlighting the vastness of the number.
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Written out, a googol looks like this: 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. The scientific notation for a googol is 1 x 10100.
In pure mathematics. In pure mathematics, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth’s up-arrow notation, Steinhaus–Moser notation, or Conway chained arrow notation .
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A googol is 10 to the 100th power, which is 1 followed by 100 zeros. While this is an unimaginably large number, there’s still an infinite quantity of larger numbers.
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