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.
Monday, 28 November 2011
Million, Billion, Trillion... Jim Loy copyright 1999