Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/494

 A R I T H M E T i e K. In working the fame example at large, the line A B Contrafled by the rule. 3.46575128)95.4327116463275(27.5518 {hows how far the operation is contraded, and how much labour is fared. ..... 6.92750I56 But here obferve, that by the rule for approximates the certain places of the quot are no more than five, 261577 viz. 27.551. And therefore, in all operations of this 242462 kind, care fhould be taken to limit the quot to fo many places certain; as is done in the following example. Examp. II. Divide 87.0763264525 by 9.365407024 j limiting the quot to four decimal places certain. 1797 9.3654017024)87.07632164525(9.2976 84.2886613216 173* 278766 66 187308 34 91458 3227 84288 7170 6555 In the above example the units of the firfl produd {landing under the place of tens, the firft figure of the quot is tens; and hence it is eafy to forelee, that fix 615 561 „ figures of the dividend retained will give four decimal places to the quot; and accordingly cut off all the other figures on the right of the dividend ; cut off like*4 becaufe, by tire wife from the divifor two figures that correfpond to Here we put a flop to the operation; rule for approximates, the next figure of the quot would them. At every new dividual, drop or omit a figure on the be uncertain. right of the divifor, and mark the figure fo dropped by We lhall conclude divifion of finite decimals with two fetting a point under it; and in multiplying the quotient- very ufeful problems. figure 7 into the divifor, fay, 7 times 7 is 49, and 3 of Prob. I. From a given multiplier to find a divifor carriage from the right, (arifing from 7X5=35), makes that gives a quot equal to the produ<ft. 52 ; fo fet down 2, and carry 5. The fame method is Rule. Divide an unit with ciphers annexed by the obferved in multiplying every other quotient-figure into given multiplier, and the quot will be the divifor fought. Examp. What divifor will give a quot equal to the the divifor. < product of 125 into the dn idend ? The fame Example at large. Given multiplier i25)i.ooo(,oo8 divifor fought. A 1000 56463275(27.55183 3.4637528)95-4327 Now, if any number be divided by .008, and the 6.92750 56 fame number be multiplied by 125, the quot and product will be equal. 261577 004 .008)7315.000(914375 quot. 242462 696 72 19114 3086 11 17318 7640 73*5 125 8 54463 36575 1731 35 14630 33 73*5 63 668232 30 34 637528 914375 predudh 24 60 56 1 32068235 103912588 40 4° 29055647 The reafon is plain: for an unit contains the quot .008 B juft 125 times ; and confequently .008 dividing any number
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