NUMERATION

, in Arithmetic, the art of estimating or pronouncing any number, or series of numbers.

Numbers are usually expressed by the ten following characters, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0; the first nine denoting respectively the first nine ordinal numbers; and the last, or cipher 0, joined to any of the others, denotes so many tens. In like manner, two ciphers joined to any one of the first nine significant figures, make it become so many hundreds, three ciphers make it thousands, and so on.

Weigelius indeed shews how to number, without going beyond a quaternary; i. e. by beginning to repeat at each fourth. And Leibnitz and De Lagny, in what they call their binary arithmetic, begin to repeat at every 2d place; using only the two figures 1 and 0. But these are rather matters of curiosity than any real use.

That the nine significant sigures may express not only units, but also tens, hundreds, thousands, &c, they have a local value given them, as hinted above; so that, though when alone, or in the right-hand place, they denote only units or ones, yet in the 2d place they denote tens, in the 3d place hundreds, in the 4th place thousands, &c; as the number 5555 is five thousand five hundred fifty and five.

Hence then, to express any written number, or assign the proper value to each character; beginning at the right hand, divide the proposed number into classes, of three characters to each class; and consider two classes as making up a period of six sigures or places. Then every period, of six figures, has a name common to all the figures in it; the sirst being primes or units; the 2d is millions; the 3d is millions of-millions, or billions; the 4th is millions-of-millions-of-millions, or trillions; and so on; also every class, or half-period, of three sigures, is read separately by itself, so many hundreds, tens, and units; only, after the lest hand half of each period, the word thousands is added; and at the end of the 2d, 3d, 4th &c period, its common name millions, billions, &c, is expressed.

Thus the number 4,591, is 4 thousand 5 hundred and 91.

The number 210,463, is 2 hundred and 10 thousands, and 463.

The number 281,427,307, is 281 millions, 427 thousands, and 307.