Monday, 28 November 2011

Million, Billion, Trillion... Jim Loy copyright 1999

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Million, Billion, Trillion...

© Copyright 1999, Jim Loy

People sometimes ask me the names of the large numbers. Here is a table. The system used in the U.S. is not as logical as that used in other countries (like Great Britain, France, and Germany). In these other countries, a billion (bi meaning two) has twice as many zeros as a million, and a trillion (tri meaning three) has three times as many zeros as a million, etc. But the scientific community seems to use the American system.

Number of zeros U.S. & scientific community Other countries
3 thousand thousand
6 million million
9 billion 1000 million (1 milliard)
12 trillion billion
15 quadrillion 1000 billion
18 quintillion trillion
21 sextillion 1000 trillion
24 septillion quadrillion
27 octillion 1000 quadrillion
30 nonillion quintillion
33 decillion 1000 quintillion
36 undecillion sextillion
39 duodecillion 1000 sextillion
42 tredecillion septillion
45 quattuordecillion 1000 septillion
48 quindecillion octillion
51 sexdecillion 1000 octillion
54 septendecillion nonillion
57 octodecillion 1000 nonillion
60 novemdecillion decillion
63 vigintillion 1000 decillion
66 - 120   undecillion - vigintillion
303 centillion  
600   centillion

See Scientific Notation.


There are other big numbers with names. A zillion has come to mean an arbitrary or unknown large number. A googol is 10^100. A googolplex is 10^googol (10^10^10^2). This number is too large to write here without exponents. Skewes' number (gesundheit) is 10^10^10^34 was used as an upper bound in a mathematical proof. Recently 10^10^10^10^10^7 was used in a proof.

The googolplex has given rise to the n-plex notation: n-plex is 10^n. n-minex is 10^-n. Donald Knuth invented arrow notation, where m^n (^ is an up arrow) is the regular m^n. m^^n is m^m^m^m...^m, with n up arrows. m^^^n is m^^m^^m...^^m, with n ^^s. According to The Book of Numbers by J.H.Conway and R.K.Guy, chained arrow notation is the following enhancement: a^^^^^b is written as a>b>5, where > is a right arrow.

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