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American vs. European Billion

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) 
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.


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, 

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   

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,   

    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   

Associated Topics:
Elementary Large Numbers
Elementary Math History/Biography
High School History/Biography
Middle School History/Biography

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