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?