Wednesday, June 3, 2015

Large Numbers With Names

The following table lists names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words". The "Traditional British" values shown are not used in American English and are becoming very rare in British English, but their other-language variants are dominant in many non-English-speaking areas, including continental Europe and Spanish speaking countries in Latin America.

          English also has many words, such as "zillion", used informally to mean large but unspecified amounts.

Standard dictionary numbers

NameShort scale
(U.S., Canada and
modern British)
Long scale
(continental Europe,
older British)

















Sexdecillion (Sedecillion)10511096


Novemdecillion (Novendecillion)106010114



In the list, scientific notation is used. For instance, a trillion is listed as  1012. This is spoken as "ten to the twelth" and written as 1,000,000,000,000. Notice that when we write big numbers, we put a comma between every third digit.

The googol Family

The names googol and googolplex were introduced in Kasner and Newman's 1940 book, Mathematics and the Imagination, in the following passage:
The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with one hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex". A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, equal to 1 with a googol zeros after it.
                   10100GoogolKasner and Newman, dictionaries
10googol = \,\!10^{10^{100}}GoogolplexKasner and Newman, dictionaries

If you wish to see a googolplex written out, here's a link you can click on, . Of course it comes in multiple volumes, each containing 1 million digits (mostly zeros) of the written out number. A googolplex is so big that if you could read 1 million volumes of 1 million digits in only a 1/1000 of a second, it would still take you MUCH longer than the age of the universe to finish.


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