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### American vs. European Billion

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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

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
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

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/

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

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