NUMERATION (Lat. numeratio, a counting, from aumerare, to count. from numcrus, num ber). The oral as opposed to the written expres sion of numbers. Numeration implies the nam ing of numerals (q.v.) and groups of numerals expressing numbers. the nomenclature thus em ployed having much to do with the efficiency of the system. Thus, if to every number there cor responded an independent name, a lifetime would not he sufficient in which to learn the munhers from one to a million. The common or decimal system proceeds by using independent names for a few of the smaller numbers and certain groups, and then repeats these names to express various numbers of groups. In this system the funda mental group is ten, independent names are given to the numbers represented by I. 2,....9, 1(1, 100, 1000, 1,000.000, and all intervening numbers are expressed by combining these names. In the evo lution of language the names of a few numbers have lost their suggestiveness, hut they are prob ably not exceptions to the regular system of for mation ; e.g. the etymologies of eleven and twelve suggest their original meaning to have been one phis ten and phis ten.
In reading numbers it is convenient to sepa rate the digits, beginning at the decimal point, into groups of three each. The groups of in tegers are then expressed by units, thousands, millions, billions, trillions, etc. Each group of integers includes three orders. viz.: (1) the order of the group itself; (2) the tens of that order; and (3) the hundreds of that order. Similarly, in each group of decimals the three orders are: (I) the order of the group itself; (2) the hun dredths of the order of the preceding group; and 3) the tenths of the order of the preceding group. Thus, for example, the number 9,321.34567 is expressed: Usage has not fully determined the names to be employed beyond hundred millions, The French and Americans call 1000 millions a bil lion; the English and Germans use the word billion to designate a million million, and so on in groups of six figures.