American vs. European Billion??

Posted: April 26, 2013 in Education, Geopolitics, Politics, Youths and Nation

Date: 07/30/2000 at 18:42:34

From: Walter

Subject: Difference between an American and a European billion I don’t know if this is really a math question but I asked myself this question during my whole school time. Even my teachers can’t answer this question.

 

The American system is:

10^06 = million

10^09 = billion

10^12 = trillion

 

The European system (formerly used in Britain, still used in Germany)

is:

10^06 = million

10^09 = thousand million

10^12 = billion

10^15 = thousand billion

10^18 = trillion

10^21 = thousand trillion

 

Why the differences? I hope you can help me.

 

Walter


Date: 07/30/2000 at 19:08:07

From: Doctor Anthony

Subject: Re: Difference between an American and a European billion The reason for the difference is historical and relates to the fact that Latin is not taught to the same extent in America as in Europe.  The bi-million, tri-million is an obvious extension from 10^6 to 10^12 to 10^18 in the European system and these become billion and trillion, respectively.

 

In America the need for a simple word for 1000 million and an absence of Latin led to the misappropriation of the word ‘billion’.  England held out for a long time with the 10^12 meaning of billion, but was eventually overwhelmed by the sheer weight of scientific and mathematical literature that used the American interpretation, so billion in England is now used in the American sense. Europe may eventually follow suit, but it will be a change from a logical system to an arbitrary one.

 

– Doctor Anthony, The Math Forum

http://mathforum.org/dr.math/


Date: 04/10/2001 at 17:12:00

From: Doctor Peterson

Subject: Re: Difference between an American and a European billion It sounds plausible, especially from a British perspective, that the “arbitrary” American system should be due to our lack of education;

but I’m not sure the charge holds up to historical investigation. I’m suspicious, in the first place, because I know from my own ancestors’ heritage that Latin was an important part of American education at

least in the 19th century, and surely also before then for those who were educated. It may be true that Latin is not taught enough here, but that has not always been true.

As our friend Jeff Miller says , first quoting D. E. Smith,

http://jeff560.tripod.com/m.html

The French use of milliard, for 10^9, with billion as an alternative, is relatively late. The word appears at least as early as the beginning of the 16th century as the equivalent both of 10^9 and of 10^12, the latter being the billion of England today. By the 17th century, however, it was used in Holland to mean 10^9, and no doubt it was about this time that the usage began to change in France. [This isn’t quite clear, but “billion” meant 10^9 in France at least by the early 18th century.]

As to the American usage, taking a billion to mean a thousand million and running the subsequent names by thousands, it should be said that this is due in part to French influence after the Revolutionary War, although our earliest native American arithmetic, the Greenwood book of 1729, gave the billion as 10^9, the trillion as 10^12, and so on. Names for large numbers were the fashion in early days, Pike’s well-known arithmetic (1788), for example, proceeding to duodecillions before taking up addition.

Further, from the OED,

The name [billion] appears not to have been adopted in Eng. before the end of the 17th c. …. Subsequently the application of the word was changed by French arithmeticians, figures being divided in numeration into groups of threes, instead of sixes, so that F. billion, trillion, denoted not the second and third powers of a million, but a thousand millions and a thousand thousand millions. In the 19th century, the U.S. adopted the French convention, but Britain retained the original and etymological use (to which France reverted in 1948).

Since 1951 the U.S. value, a thousand millions, has been increasingly used in Britain, especially in technical writing and, more recently, in journalism; but the older sense “a million millions” is still common.

Putting this together, we see that the “American” use of “billion” originated not here but in France; and that it was probably based not on stupidity, but on practicality (another well-known characteristic of Americans), as there was more need for a name for 10^9 than for 10^12. There _is_ logic behind the usage; in this system, billion doesn’t mean “million squared” but “second -illion” counting by thousands. It’s hardly different from deciding whether to index arrays starting at 0 or 1. You just have to choose where to start and how big a step to take, and the numbers follow a logical progression.

I fully agree that the original British usage is nicer and easier to explain, and I wish it were the standard system; but the other is not really arbitrary. It should also be noted that France, not Britain, was the center of mathematical scholarship at the time “billion” was imported into America, so it can be reasonably suggested that the Americans adopted it for the same reason the British have more recently: it was used by the most important writers.-Doctor Peterson

http://mathforum.org/dr.math/

http://mathforum.org/library/drmath/view/52579.html

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