Difference between revisions of "Large numbers"

Revision as of 21:26, May 23, 2007

American	European	Math
thousand	thousand	10³ = 1,000
million	million	10⁶ = 1,000,000
billion	thousand million	10⁹ = 1,000,000,000,000
trillion	billion	10¹² = 1,000,000,000,000,000
quadrillion	thousand billion	10¹⁵ = 1,000,000,000,000,000,000
quintillion	?	10¹⁸ = 1,000,000,000,000,000,000,000

@@ Line 1: / Line 1: @@
-Confusingly, there are two systems for naming numbers using the ending ''-illion.'' The history of which system has been used in which countries at which times is complex.
-In both systems, a "million" means a thousand thousands or 10<sup>6</sup>.
-Above the "million," one system introduces a new name for each new group of ''three'' zeroes. In particular, a "billion" means a thousand millions. This system is used in the United States and has been for a long time.
-Another system introduces a new name for each group of ''six'' zeroes. Thus, a billion means a million millions. This used to be British usage, ''but no longer is;'' newspapers and official government reports now use the same system as the U. S., and this system is the one now taught in British schools. Some older Britons remain attached to the older usage.
-This system in which the word ''billion'' means 1,000,000,000,000, though not used England, is used in many European countries.
-The word ''milliard,'' is unambiguous: it always means 1,000,000,000. It is rarely used in countries where a ''billion'' means the same thing. (Though rarely used, it is found in both British and American dictionaries and is thus a legitimate English word).
-As a practical matter, it is important to be aware of the difference in meaning when reading old material, and to avoid using either set of names&mdash;especially the common but ambiguous ''billion''&mdash;in any context where misunderstanding can occur.
-In technical or scientific writing, the problem does not arise because it is customary to use scientific notation (''10<sup>12</sup>'') or SI prefixes (''tera-'').
 {|border=1
 |-
-| U. S. usage || Former British usage || Math
+| American || European || Math
 |-
 | thousand || thousand || 10<sup>3</sup> = 1,000
@@ Line 23: / Line 7: @@
 | million || million || 10<sup>6</sup> = 1,000,000
 |-
-| billion || thousand million or milliard || 10<sup>9</sup> = 1,000,000,000
+| billion || thousand million || 10<sup>9</sup> = 1,000,000,000,000
 |-
-| trillion || billion || 10<sup>12</sup> = 1,000,000,000
+| trillion || billion || 10<sup>12</sup> = 1,000,000,000,000,000
 |-
-| quadrillion || thousand billion or (very rarely) billiard || 10<sup>15</sup> = 1,000,000,000,000
+| quadrillion || thousand billion || 10<sup>15</sup> = 1,000,000,000,000,000,000
 |-
-| quintillion || trillion || 10<sup>18</sup> = 1,000,000,000,000,000
+| quintillion || ? || 10<sup>18</sup> = 1,000,000,000,000,000,000,000
 |}
-Words for numbers above 10<sup>18</sup> may be found in dictionaries or tables of number names, but are almost never used. For years, mathematicians and computer scientists have enjoyed a sort of game of inventing systems for naming large numbers, but there is no practical need to render such names as words, and it is very questionable whether any of them should be considered to be "real" words; they are seldom encountered outside of discussions of large numbers and number naming.
-The name ''googol,'' for a 1 followed by a hundred zeroes, i.e. 10<sup>100</sup>, was popularized by a 1940 popular book on mathematics, Kasner and Newman's classic ''Mathematics and the Imagination.'' It was invented by Kasner's nine-year-old nephew. It and Kasner's own ''googolplex'' (a 1 followed by googol of zeroes) have entered the language, but are only used figuratively. The word ''googol'' was the inspiration for the name of the search service ''Google.''

Difference between revisions of "Large numbers"

Revision as of 21:26, May 23, 2007

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