The figure o is called nought or nothing because it has no value in itself. The other nine characters are called significant figures, because each has a value of its own. The ten Arabic characters used singly can only express the numbers that correspond to their names; but when two or more of them are placed together, they serve to express any number whatever. In order to illustrate the principle of the Arabic notation, we will suppose that a stationer has a quantity of pencils, consisting of seven boxes, nine bundles, and four single ones, and that there are as many bundles in a box as there are single pencils in a bundle. If each bundle contain a dozen pencils, then each box will contain a dozen bundles, or a gross of pencils; and consequently the whole number of pencils will be 7 gross 9 dozen 4 units. If, however, each bundle contain only ten pencils, then each box will contain ten bundles, or a hundred pencils; and in this case the number will be 7 hundreds 9 tens 4 units. Now, any number of pencils, tops, marbles, &c., or even abstract numbers, may be expressed in units, dozens, dozens of dozens, &c., or units, tens, tens of tens, &c.; or by any similar progression founded on any number whatever. The method of expressing numbers by the progression founded on the number ten is almost universally adopted. It is called the decimal method (from decem, the Latin for ten), and is supposed to have had its origin in the great facility. for counting which is afforded by our ten fingers, and hence the characters o, 1, 2, 3, 4, 5, 6, 7, 8, 9, are sometimes called the ten digits (from digitus, the Latin for a finger). SECTION II.-NUMBERS OF TWO FIGURES. If a quantity of pencils consist of five bundles of ten, and seven single ones, instead of expressing the number thus 5 tens 7 units, we may omit the words tens and units, which are the denominations of the figures, and write only 57, with the understanding that the 5 being placed before the other figure, stands for five tens or fifty; and therefore 57 will stand for fifty-seven. Hence 10 will stand for 1 ten o units, or ten. (12) four. B. (8) five; (9) one; &c. (5) nine; seven; (4) three ; Sixteen; (2) thirteen; (3) seventeen ; (fifteen; (10) (7) (5) eleven; (nineteen; " twelve; (8) fourteen; (0) eightten; sixteen ; (12) eleven; (13) nineteen ; thirteen ; (15) twelve. teen ; (14) (8) (5) () (3) C. Twenty-four; "twenty-seven; " twenty-one; twenty-six; thirty-eight; "thirty-four; "thirtynine; forty-eight; forty-three; () forty; (1) fifty(sixty; (12) fifty-four; (14) seventy-four; (15) seventy-nine; (1) eighty-three; (17) eighty-five ; (1) ninety-seven ; (19) ninety; (20) ninety-nine. Express in words seven ; D. (1) (3) 7 2 (9) (11) (13) 9 3 9 4 (15) 4 7 8 (14) 6 (5) 13 15 19 12 ΙΟ 19 12 (2) (4) 17 II (6) 18 13 In the last section we explained that a figure placed before the units' figure stands for tens, that is, tens of units. We will now place a figure before the tens, and suppose, as before, that it stands for tens of the denomination of the figure before which it is placed, that is, for tens of tens, or hundreds ; hence 357 will denote 3 hundreds 5 tens 7 units, or three hundred and fifty-seven. Similarly 100 will stand for 1 hundred o tens o units, or one hundred. IOI will stand for 1 hundred c tens 1 unit, or one hundred and one. 102 will stand for 1 hundred o tens 2 units, or one hundred and two. 110 will stand for 1 hundred 1 ten o units, or one hundred and ten. B III will stand for 1 hundred 1 ten 1 unit, or one hundred and eleven. 112 will stand for 1 hundred i ten 2 units, or one hundred and twelve. 113 will stand for 1 hundred 1 tén 3 units, or one hundred and thirteen. 120 will stand for 1 hundred 2 tens o units, or one hundred and twenty. 137 will stand for 1 hundred 3 tens 7 units, or one hundred and thirty-seven. 429 will stand for 4 hundreds 2 tens 9 units, or four hundred and twenty-nine. 506 will stand for 5 hundreds o tens 6 units, or five hundred and six. 830 will stand for 8 hundreds 3 tens o units, or eight hundred and thirty. &c. Although the figure o has no value in itself, it is important to remember that it increases the value of another figure when written after it; though it does not alter the value of a number when placed before it. Thus, 57 denotes 5 tens 7 units, or fifty-seven ; but 570 stands for 5 hundreds 7 tens o units, or five hundred and seventy. Again, 49 stands for 4 tens 9 units, or forty-nine; and 049 denotes o hundreds 4 tens 9 units, that is, 4 tens 9 units, or forty-nine, the same as before. In the same way it may be shown that o may be omitted before a number, but not after it, without altering the value of the number. Examples.-Express in words G. (1) 134 (2)182 (8) 156 (1) (10) (18) 166 (16) 180 (17) (11) (14) 141 119 ΙΟΙ (12) 198 137 (15) 199 7109 (18) 190 Express in figures— (12 (7) I. One hundred and sixty-three; () one hundred and eighty-seven; one hundred and thirtyfour; (4) one hundred and forty-nine; one hundred and thirty; one hundred and twenty-eight; "" one hundred and twelve; one hundred and nineteen ; (3) one hundred and eleven; (10) one hundred and (11) one hundred and one; twenty; one hundred and fifty; (13) (14) one hundred and five; one hundred and eighty-nine; (15) one hundred and ten. J. Four hundred and seventeen ; (2) two hundred and sixty-four ; (3) nine hundred and eleven ; (4) seven hundred and seventeen; (5) six hundred and twenty; eight hundred and eighty; hundred and ninety-nine; twelve; nine four hundred and (10) two hundred (12) five hundred (9) two hundred and twenty; and two; (11) five hundred and six; and sixty; (13) six hundred and fifty; (six hundred and five. Express with three figures (2) K. Eighteen; (2) eleven; " twenty-three; "" fortyseven; (5) ten; (6) ninety-four; thirty; ") eighty-six ; (?) twelve; four; (11) (12) twenty; seven; (13) sixty; (14) eight; (5) twenty-five; (16) eleven; 7) eighty-one; (18) seventeen (19) seventy-one : (20) ninety; (21) (22) seventy. 1; one; SECTION IV.-NUMBERS OF FOUR OR MORE FIGURES. A figure to the left of the hundreds' figure stands for tens of hundreds or thousands; it is generally |