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googol and googolplex

What are googol and googolplex?

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. One such number is googolplex, which is 10 to the power of a googol, or 1 followed by a googol of zeros.

The word googol was introduced in Mathematics and the Imagination, a book written by Edward Kasner and James R. Newman in 1940 to survey the field of mathematics for the layperson. Kasner was a mathematician at Columbia University and Newman was both a mathematician and a practicing lawyer in the state of New York.

As explained in the book, Dr. Kasner's 9-year-old nephew, Milton Sirotta, came up with the word googol when asked to think of a name for 1 followed by 100 zeros. In the same book, the authors introduced another big number -- one so large that it cannot even be written. This number was given the name googolplex and is defined as 10 to the power of a googol, or 1 followed by a googol zeros.

Why do googol and googolplex have names while most other big numbers do not?

Giving names to these two huge numbers was a didactic technique used by two mathematicians to pique the interest of laypeople in the differences between very large numbers and infinity.

A few absurd thought experiments help demonstrate the size of these numbers. Given any reasonable estimate of the size and age of the universe, there's neither enough space to write all the zeros in a googolplex, nor the time to do so. If every part of the universe were filled with zeros, there still would be nowhere near enough space to hold them all. And, if all the supercomputers in the world today had been put to the task at the beginning of the universe -- 16 billion years ago, by most estimates -- they couldn't generate anywhere near that many zeros.

It would be impossible to assign names to all other large numbers, as there's an infinite number of them.

How many zeros are in a googol? A googolplex?

A googol is written as follows:

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

However, as explained above, a googolplex has so many zeros that it can't be written.

What's bigger than a googolplex?

Even though a googolplex is immense, Graham's number and Skewes' number are much larger. Named after mathematicians Ronald Graham and Stanley Skewes, both numbers are so large that they can't be represented in the observable universe.

What is Google's connection to googol and googolplex?

In 1998, Sergey Brin and Larry Page registered their new company under the name Google, which was a misspelling of the word googol. Brin and Page explained that this name fit with their goal of building very large-scale search engines. To bring the point home, they named their corporate headquarters the Googleplex.

Many networking tasks require converting binary to decimal. Learn how to make the conversion in this tutorial.

This was last updated in August 2022

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