SECTION II. NUMERATION. 38. Numeration is the general method of reading and writing numbers. 39. As there is no end to the formation of new orders on the left, and as it would, even in ordinary numbers, be inconvenient to give a new name to each new order, the figures of large numbers are separated into periods of three figures each. Thus, beginning at the right hand, and proceeding towards the left, we separate, by a comma, the first three figures, which constitute the first period. Then, proceeding towards the left, we separate three more, and so on, regularly, till the whole of the figures are thus separated. As the number may consist of any number of figures, it is evident that the lefthand period will often contain only one or two figures. 40. The first, or right-hand period, is called Units; the next Thousands; the next Millions; and so, in succession, Billions, Trillions, Quadrillions, Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecillions, Octodecillions, Novendecillions, Vigintillions, Viginti-unillions, Viginti-billions, &c. 41. To facilitate the remembrance of the names of the periods, to show their import and relative position in the scale of numbers, as well as to extend them as far as required by any number within the scope of human thought or calculation, the following Table of Latin Numerals, from which they are nearly all derived, will be found very useful. From this Table we also derive the names of some months; and there is this singularly coincident irregularity, viz., that as the Romans began their year in March, the month September was, as its name denotes, in their Calendar, the Seventh; whereas, in ours, to which the name has been transferred, -and which begins two months earlier, it is the Ninth: so, also, in the scale of the periods, as we have two names, Units and Thousands, which do not belong to the regular nomenclature, in which we may suppose that the name Millions has been substituted for Unillions; the period Billions, which, from the import of the word, should be the second, is the fourth, and, consequently, Septillions, which should be the seventh, is the ninth period. 42. To correct this discrepance, therefore, we must, in applying the Table, add 2 to the number corresponding to the name of the period, (or month,) which will give its order; or subtract 2 from the number showing its order, which will give the number corresponding to its name. Thus, for exam、 ple, if I would know the order of the period Octillions or the month October; as octo is eight, I add 2, which makes 10; I therefore say, that Octillions is the tenth period, and October, the tenth month. 43. Again if I wish to know the name of the twelfth period, I subtract 2 from 12, and I have 10; which, in Latin, is decem: I therefore say, that the name of the twelfth period is Decillions. 44. By means of the table we may continue the nomenclature of periods, thus: viginti-trillions, &c. to viginti nonillions; trigintillions; triginta-unillions, triginta-billions, &c.; quadragentillions; quadraginta-unillions, &c.; quinquagentillions; sexagentillions; septuagentillions; octogentillions; nonagentillions; centillions. 45. The above Table, as well as the names of the periods in the Scale of Numbers, we could easily extend, but such extension could, for our present purpose, be of no utility; seeing that the number 1 centillion is far above the scope of human affairs or conception. For, if we suppose a hollow globe, ten millions of millions (10 trillions) of miles in diameter, to be filled with dust, so fine that there should be one thousand millions (1 billion) of particles in each cubic inch; the whol number of particles in this mighty mass would be an inconceivably small part of a centillion. 46. It is plain (see Art. 36) that, whatever may be the value of the units composing any figure in the scale, the next figure on the left will be tens, with regard to that value, and the next hundreds. Wherefore, in each period, going from right to left, we say units, tens, hundreds: that is to say, with respect to the digits, any figure on the right is a number of units; in the middle, a number of tens, and on the left, a number of hundreds. Hence, we read the number, under any period, as if it stood alone, except merely at last pronouncing the name of the period. Thus, the number 243 is read two hundred and forty-three, under whatever period it may stand. For example, in the following number: M. Th. U. 243 243 243 Beginning at the left, we say, two hundred and forty-three Millions; two hundred and forty-three Thousand; two hundred and forty-three. 47. Hence also, by its place, we easily determine the value of each figure in a number, without reference to the others. Thus, in the above, beginning at the left, the figure 2 is read, first, two hundred Millions; then, two hundred thousand; and, lastly, two hundred. The figure 4 is, first, forty Millions; then, forty Thousand; and, lastly, forty. The figure 3 is, first, three Millions; then, three Thousand; and, lastly, three. 48. Again: from the same universal law, it is evident that we can, in a large number, read a part, consisting of a number of consecutive figures, taken at pleasure, (the left-hand figure of such part being significant,) as a number of units of the order signified by the place of the right-hand figure of the part taken. Thus, in the number B. M. Th. U. 128 029 625 343 One hundred and twenty-eight Billions; twenty-nine Millions; six hundred and twenty-five Thousand, three hundred and forty-three: taking the figures two and two in order, we read, twelve tens of Billions; eighty hundreds of Millions; twenty-nine Millions; sixty-two tens of Thousands; fifty-three hundreds and forty-three: or, four and four, we read, one thousand two hundred and eighty hundreds of Millions; two thousand nine hundred and sixty-two tens of Thousands; five thousand three hundred and forty-three: or, taking the two middle figures, we read, ninety-six hundreds of thousands: or, taking eight figures, beginning with the figure 8, we read eighty Millions, two hundred and ninety-six Thousand, two hundred and fifty-three hundreds, or any other part in the same manner, at pleasure. 49. From the above, we easily perceive that any number, having a significant figure in the place of units, may be considered as a binomial; (bis, twice, and nomen, name ;) that is, as consisting of two names or parts, one of which is the number of tens expressed by all the figures on the left of its unit figure; and the other the number of units expressed by that figure. Thus, the above number, considered as a binomial, consists of twelve Billions, eight hundred and two Millions, nine hundred and sixty-two Thousand, five hundred and thirty-four tens and three units. This general binomial property will be found important in some of our future details. 50. When some of the intermediate orders or periods of a number contain ciphers only, we omit such orders or periods in reading, as also the name Units: because, all numbers being composed of units, that name is applicable to any order or period. Thus, the following number, B. M. Th. U. 1 000 009 022 is read One Billion; nine Thousand and twenty-two. Let the following numbers be expressed in words: 1. 101 4. 1001 7. 10010 10. 900090 19. 111617125198423514891 20. 83006500010110099580000428 51. When familiar with the Table, and the names derived from it, we dispense with actually pointing the periods and writing their names. Thus, in the number 65428075000095008 beginning at the right hand and taking the figures three at a time, we count the number of periods, saying, 1, 2, 3, 4, 5, 6, and (42) subtracting 2, we have 4 for remainder, by the Table quatuor, and hence, quadrillions, for the name of the highest period. Wherefore, having in this the figures 65, we read sixty-five Quadrillions; four hundred and twenty-eight Trillions; seventy-five Billions; ninety-five Thousand and eight. To read this as a binomial, we begin with the tens in counting the periods; and finding 6 only in the highest, we say, six Quadrillions; five hundred and forty-two Trillions; eight hundred and seven Billions; five hundred Millions; nine thousand five hundred TENS, and eight UNITS. In like manner, let each of the following numbers be read as a Natural and as a Binominal Number: 1. 2986400032504003 2. 1000078540003205 3. 98000043587020050076 4. 6850685006850006850000685 Let the following number be read in parts, taking the figures consecutively two and two, four and four, and five and five, as in Art. 48: 64026402640264026402 52. To express, in figures, a large number given in words, we first write the names of the periods, beginning with Units and ending with the highest or first name mentioned in the reading. Then, beginning with the left-hand period, we write its number underneath, as if it were to stand alone. As we progress from left to right, the order of the places is, under each period, hundreds, tens, units; consequently, in writing its number, we first consider whether it contains hundreds, and write a cipher or digit in the left-hand place accordingly. We next consider whether it contains tens; and write, accordingly, a cipher, or digit in the middle place. Lastly, in like manner we supply the place of units. If, in the reading, any period is wanting-that is, not mentioned-we must, of course, write 000 under it. The cipher is of no use, when placed on the left of all the significant figures; because, in this situation, it does not show their position towards the left. To express, in figures, the number Forty Quintillions; ten Quadrillions; two Billions; ten Millions; eleven Thousand, four hundred and twelve; we first write, as above directed, the names of the periods, 010 Quintillions Quadrillions Trillions Billions Millions Thousands Units. 40 000 002 010 011 412 Then, as the number first dictates Forty Quintillions, we write 40 under Quintillions, as if it were to stand alone. Next, for the ten Quadrillions, as this number contains no nundreds, we first write 0 in the place of hundreds; then, as ten is expressed by a unit in the place of tens, we write 1 in that place. Lastly, as there no units, we write 0 in the place |