Monday, July 21, 2008

When is a billion not a billion?


In an internal business meeting today, I was joking about my dubious relationship with numbers—I mix them up easily—when I mentioned a fact that no one in the room was aware of. Until fairly recently, an American billion was not the same as a British billion. What we called a billion, they called a milliard; and what we called a trillion, they called a billion. I'm pretty sure I first heard of this years ago when I stumbled upon the following passage in the Merriam-Webster dictionary:
The American system of numeration for denominations above one million was modeled on the French system but more recently the French system has been 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 the first denomination above 1,000 millions (the British milliard) is 1,000 times the preceding one, but each of the denominations above 1,000 milliards (the British billion) is 1,000,000 times the preceding one (one trillion = 1,000,000 billions; one quadrillion = 1,000,000 trillions).

That's still what it says now, despite the fact that, according to Wikipedia, our brothers in the UK adopted the "American" system way back in 1974.
For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so that usage of the two systems was often referred to as "British" and "American" respectively. In 1974 the government of the UK abandoned the long scale, so that the UK now applies the short scale interpretation exclusively in mass media and official usage. Although some residual long-scale usage still continues, the terms "British" and "American" no longer represent accurate terminology.
The more accurate way to refer to these two numerical systems are long scale and short scale. The short scale (in which a billion is a thousand millions) is now used primarily by English-speaking countries (plus, for some reason, Brazil), and the long scale (in which a billion is a million millions) by the rest of the world. To keep things interesting, some countries use the short scale but keep the word "milliard" from the long scale (e.g.: Russia, Israel, Turkey, Iran), while others use a completely different numbering system all together.

China, Japan and Korea use a system based on myriads. Myriad is the Classical Greek name for the number 10,000. I remember this from my time in Japan: 20,000 yen was ni-man 'en (or two ten-thousands). In the Chinese system, which Japan and Korea use, the new denominations come every four places, instead of every three or every six. Therefore, in Japanese, 10,000 man is an oku (1,0000,0000, or what we would call a hundred million) and 10,000 oku is a chou (1,0000,0000,0000, or what we could call a trillion and a Frenchman would call a billion). Whew!

The Indian numbering system, used in India, Pakistan, Bangladesh, Nepal and Myanmar, creates a new denomination every two decimal places after a thousand. This means that a lakh is 1,00,000 (our one hundred thousand), a crore 1,00,00,000 (our ten million) and arawb 1,00,00,000 (an American's billion or a Frenchman's milliard).

So, in a nutshell, the denominations in the various numbering systems are, for the most part, defined thusly:
Short scale: 100 (one), 101 (ten), 102 (a hundred), 103 (a thousand), 106 (a million), 109 (a billion), 1012 (a trillion), 1015 (a quadrillion), 1018 (a quintillion)...

Long scale: 100 (one), 101 (ten), 102 (a hundred), 103 (a thousand), 106 (a million), 109 (a thousand millions, or a milliard), 1012 (a billion), 1015 (a thousand billions, or a billiard), 1018 (a trillion)...

Chinese: 100, 101, 102, 103, 104, 108, 1012, 1016, 1020...

Indian: 100, 101, 102, 103, 105, 107, 109, 1011, 1013...
I guess the next thing to do would be to explain why in French, their word for 78 translates to "sixty-eighteen" and 92 is "four twenties and twelve." Maybe just for laughs.

Labels: , ,