Tuesday, May 1, 2012

The Scale’s the Thing

In a way it pleases me that some nations drive on the left, some on the right, that some homes hang the toilet roll so that the sheet comes from the back, others so it unfurls up front. It pleases me that the metric hasn’t conquered all and that the inch still survives. Vive la difference.

Yesterday I quoted a bit of verse using the word milliard; Brigitte’s comment pointed out that we don’t use that number here. It is European. She wondered about the difference.

Well, according to the French, who claim to have invented both ways of naming numbers, it has to do with the scale that you use. There is a long scale and a short. The long scale is used in most of Europe, the short scale in  the United States, Britain, and most English-Speaking countries, but the British made the switch from long to short relatively recently (1974), when Prime Minister Harold Wilson told parliament that in government statistics billion, henceforth, would mean 109, as is common in our usage, rather than 1012 as had been the case in Britain theretofore.

The long scale is the older of the two and was formulated by the French mathematician Nicolas Chuchet (approx. 1445-1488). The short scale was developed in the seventeenth century by  French mathematicians bent on reform and became very influential by the nineteenth. In the long scale, as shown below, actual names are attached, after the million, only to numbers that are multiple of a million (6 zeroes)—the only exception being the first in the series. The short scale has names for multiples for each thousand of millions. Here the two schemes.

Long Scale
Short Scale
No. of Zeroes
million
million
6
milliard
billion
9
billion
trillion
12
thousand billion
quadrillion
15
trillion
quintillion
18
thousand trillion
sextillion
21
quadrillion
septillion
24
thousand quadrillion
octillion
27
quintillion
nonillion
30
thousand quintillion
decillion
33
sextillion
undecillion
36
thousand sextillion
duodecillion
39
septillion
tredecillion
42


The long scale is using the Latin for two, three, four, etc. to designate multiplications by millions; thus a million x million is a billion, a million x million x million is a trillion, and so on. The names thus indicate how many times to multiply a million’s six zeroes to get the size of the number: billion is 2 x 6, trillion is 3 x 6 zeroes. Numbers that fall between these don’t have names of their own. The short scale advances by multiplying the previous number in the scale by 1,000. The names, in effect, indicate how far down the short scale that you are. A way to use them is to exploit the multiplicand, 1,000, with its three zeroes. We use the name to multiply 3—then add 3 to get the number of zeroes. Thus, sextillion: 6 x 3 = 18 + 3 = 21 zeroes or 1021.

The long scale is odd only because its first number after million (milliard) is only a multiple of 1,000; all others are multiples of millions. The short scale is more consistent, always advancing by three zeroes, but, unfortunately, it uses the old names from the long scale. Thus octillion, in that system, has 27 zeroes, and what exactly does that have to do with eight?

1 comment:

  1. Ha! If I were a rich one...(you may hum now), I'd prefer to be called a billionaire in Germany. There my wealth would be described by 13-digits, beating the 10-digit wealthy American, Canadian or English woman. Am I displaying my internal competitor?

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