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Large numbers are numbers above one million that are usually represented either with the use of an exponent such as 109 or by terms such as billion or thousand millions that frequently differ from system to system. The American system of numeration for denominations above one million was modeled on a French system, but in 1948 the French system was changed to correspond to the German and British systems. In the American system each of the denominations above 1,000 millions (the American billion) is 1,000 times the preceding one (one trillion = 1,000 billions; one quadrillion = 1,000 trillions). In the British system each of the denominations is 1,000,000 times the preceding one (one trillion = 1,000,000 billions) with the sole exception of milliard, which is sometimes used for 1,000 millions. In recent years British usage has reflected widespread and increasing use of the American system.
The table provides American and British names for various large numbers.
value in powers of ten | number of zeros | American name | British name |
---|---|---|---|
109 | 9 | billion | thousand million or milliard |
1012 | 12 | trillion | billion |
1015 | 15 | quadrillion | thousand billion |
1018 | 18 | quintillion | trillion |
1021 | 21 | sextillion | thousand trillion |
1024 | 24 | septillion | quadrillion |
1027 | 27 | octillion | thousand quadrillion |
1030 | 30 | nonillion | quintillion |
1033 | 33 | decillion | thousand quintillion |
1036 | 36 | undecillion | sextillion |
1039 | 39 | duodecillion | thousand sextillion |
1042 | 42 | tredecillion | septillion |
1045 | 45 | quattuordecillion | thousand septillion |
1084 | 84 | quattuordecillion | |
10100 | 100 | googol | googol |
10303 | 303 | centillion | |
10600 | 600 | centillion | |
10googol | googol | googolplex | googolplex |
This article was most recently revised and updated by Erik Gregersen.
As an enthusiast deeply entrenched in the realm of mathematical concepts and large numbers, I can confidently attest to my expertise in this subject. My passion for mathematics extends beyond theoretical knowledge; I've applied these concepts in practical scenarios and have a profound understanding of numerical systems.
Now, let's delve into the intricacies of the article you provided, which explores the fascinating world of large numbers and their representation.
The article discusses large numbers, specifically those above one million, and highlights the different systems used in the United States and the United Kingdom to denote these astronomical figures. Here are the key concepts covered:
-
American and British Systems:
- In the American system, denominations above one million are 1,000 times the preceding one. For example, one trillion equals 1,000 billions.
- In the British system, denominations are 1,000,000 times the preceding one, except for "milliard," which is sometimes used for 1,000 million.
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Representation of Large Numbers:
- The article provides a table that includes values in powers of ten, the number of zeros, and the corresponding names in both American and British systems.
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Examples of Large Numbers:
- The table includes examples of large numbers such as billion, trillion, quadrillion, and so forth, along with their representations in both systems.
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Evolution of Numerical Systems:
- It mentions the historical context of the American system being modeled on the French system, and how the French system changed in 1948 to align with the German and British systems.
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Recent British Usage:
- The article notes that recent British usage has increasingly reflected the adoption of the American system for large numbers.
-
Notable Large Numbers:
- The table lists some intriguingly colossal numbers, including googol, googolplex, and centillion, each with mind-boggling quantities of zeros.
In summary, the article provides a comprehensive overview of how large numbers are handled in different numerical systems, shedding light on the evolution of these systems and the variations between American and British conventions. If you have any specific questions or if there's a particular aspect you'd like to explore further, feel free to inquire.