9,86540 7024)87,07632164525(9,2976 278766 187308 91458 84288 7170 6555 615 561 54 Here we put a stop to the operation, because, by the rule of approx imates, the next figure of the quotient would be uncertain. I shall conclude division of finite decimals with two very useful problems. PROBLEM 1st. From a given multiplier to find a divisor that gives a quotient equal to the product. RULE. Divide an unit with cyphers annexed by the given multiplier, and the quotient will be the divisor sought. EXAMPLE. What divisor will give a quotient equal to the product of 125 into the dividend? OPERATION. Given multiplier, 125)1,000(,008 Divisor sought. 1000 Now, if any number be divided by ,008, and the same number be multiplied by 125, the quotient and product will be equal. Thus ,008)7315,000(914375 The reason is plain to the meanest capacity, for an unit contains the quotient ,008 just 125 times, and consequently ,008 dividing any number will give a quotient 125 times greater than the dividend; that is, the quotient will be equal to the product of the dividend multiplied by 125. PROBLEM 2nd. From a given divisor to find a multiplier that gives a product equal to the quotient. RULE. Divide an unit with cyphers annexed by the given divisor, and the quotient will be the multiplier sought. EXAMPLE. What multiplier will give a product equal to the quotient arising from the same number divided by 008. Given divisor, ,008)1,000(125 Multiplier sought. 8. 20 16 40 40 Now if any number be multiplied by 125, and the same number be divided by 008, the product and quotient will be equal, as appears in the following If a finite divisor divide a repeating dividend, work as in whole numbers, but in continuing the division, instead of annexing cyphers to the remainder, annex the repeating figure of the dividend. From Ex. 2 and 4, we may learn, that the quotient does not always begin to repeat when the repeating figure of the dividend is taken down; and from Ex. 5, that the quotient sometimes comes out a circulate. In Ex. 5 and 6, the cyphers in the divisor on the right hand are cut off; but the place of the first quotient figure is determined by that figure of the dividend which would have stood over the units of the first product, had the cyphers been retained. RULE 3d. If a finite divisor divide a circulating dividend, work as in whole numbers; but in continuing the division, instead of annexing cyphers to the remainder, annex the circulating figures of the dividend. [carried up. 92 [brought up. 92 278 260 185 130 *557 If the divisor be interminate, reduce it to a vulgar fraction, as will be taught in reduction of decimals; then multiply the given dividend by the denominator, and divide the product by the numerator. Here are six cases, for the divisor may either repeat or circulate, and may divide a finite, a repeating, or circulating dividend. |