Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/493

 ARITHMETICS:. 4n riage may, in feme cafes, effect feveral columns on the In Var. 2. the unit 3 (lands under the place of ten* left, and thereby render more figures of the quot uncerthoufands, and fo 9 is ten-thoufands; and to the re- tain than rule pteferibes. The fureft way, there* mainder o annex .00, for the two decimal places in fore, is, tothemake two operations with contrary figns, the divifor; then-dividing, you get 00 to the quot; and and then the figures in which the two quots agree are becaufe 9 (lands in the place of ten-thoufands, the quot continues to be wholly integers. The procefs is the fame certain. , In order to make the reafon of the rule appear, it will in Var. 3. and 4. Laftly, we (hall allow decimal places to both dividend be neceifary to work an example. and divifor. Example. Var. 1. for. 2. A 3-5)320.95(91,7A 3-5)3*-095(9-i7 31.5*Si-S” 42.9723+)nio.79 286078—{25.849, 85944 6* • • • 59 35 3T 68 21486 >5 245 245 245 245 3648 536 Var. 3; 3437 784 Var. 4. •35)-32oo5(.9i7 3-5)-32095(.09i7 210 3*15" 3 M' * 17 49 59 35 35 245 245 18780 245 245 In Var. 1. the units of the firfl produft (land under tends of the dividend; and fo 9, the firft figure of the Here we (lop, no more places being certain.' The quot, is tens. In Var. 2. the units of the.firft product reafon is obvious; for the right-hand figure of the firft (land under units of the dividend, and fo 9 is units. In product, viz. 6, is uncertain; and confequently all the Var. 3. the units of the firft produd (land under primes, figures under it, on the right of the line A B, will be and fo 9 is primes, &c. fo too ; that is-, the laft remainder and new dividual are To divide.by 10, 100, 1000, is to move the deand of courle the figure that would go next cimal point one place toward •» he left for every cipher in touncertain, the quot. the divifor. From this example it appears, that all the figures on Thus, And Thus,the right of the line A B are uncertain and ufelefs; if io)768( 76.81 10)17.a8( 1-728 therefore a way of working, without writing down thefe ioo')768( 7.68 I 100)17.28( .1728 ufelefs figures, can be found, we-(hall then have a meiooo)768( 768 I 1000)17.28( .01728 thod of dividing long decimals, whether finite or approxiioooo)768(.o768 l 10000)i7.28(.ooi728 mate, fo as to contradt the operation, and limit the produft to any number of decimal places propofed. And i this may be effedfed by obferving.the following Approximates; Rule. Write the produdt of the firft quotient-figure In dividing approximates; the certain'places -of the under the dividend ; and from the fituation of the units quot may be determined by the following place, confider how many figures of the dividend muft Rule. Place the divifor under the-firft dividual, to give the quot the number of decimal and the number of certain figures in the* quot (hall be beplacesretained cut off the other figures on the right, one lefs than the number of places from the left of the and alfointended; the correfponding to them on the right divifor to the firft + or —, whether in the divifor or in of the divifor;figures then fubtradl; efteem this and every folthe dividend. lowing remainder a new dividual; and for each new diEx. 1. E'x. 2. drop a figure on the right of the divifor; but in Dividend 1110.79286078— Dividend mo.7929— vidual multiplying the quotient-figures into the divifor, take in Divifor 42.9723+ Divifor 25.8490136 + carriage from the right hand; as in the fallowing Certain places five, where- Certain places fix, where- the examples. of three are decimals. of four are decimals. T Divide b But here it is to be obferved, that the uncertain car- and?.r'limit- the quot to95-43275-<M3275 four decimal places.7 3-4637528; : Contracted
 * 59 '
 * 25134