From 84 take 82.3412 Answer 1.6588 Multiplication of DECIMALS Place the multiplicand and multiplier, after any manner under each other; and having multiplied as in whole numbers, cut off as many places of decimals in the product, counting from the right hand towards the left, as there are in the multiplicand, and multiplier ; but if there be not a suffici. ent number of places in the product, the defect may be supplied, by prefixing cyphers thereto. For the denominator of the product, being an unit, prefixed to as many cyphers, as the denomi. nators of the multiplier and multiplicand contain of cyphers, it follows that the places of decimals in the product will be as many as in the numbers from whence it arose. Multiply 121.6 by 2.76 2.76 7296 8512 2432 Answer 335.616 Multiply .0089789 by 1085 Answer 9.7421065 Multiply .248723 by .13587 Answer .03379399401 Division of DECIMALS. Having divided as in whole numbers, annexing cyphers to the dividend if they be wanted; the decimal places in the divisor and quotient must be equal to those in the dividend, and the defect supplied by prefixing cyphers to the quotient. For the dividend is a product, contained under the divisor and quotient; and that product contains as many places of decimals as the numbers do from whence it arose : therefore, the difference between the number of decimals in the dividend and divisor, must be cut off in the quotient. E X A M P L E S. Divide .144 by .12 .12).144(1.2 24 Divide 63.72413456922 by 2718 2718)63.724134569220.02344522979 9364 12101 12293 14214 6245 8096 26609 21472 24462 Answer .02344522979 There being 11 decimal figures in the dividend. and none in the divisor, 11 figures are to be cut off in the quotient; but as the quotient itself consists of but 10 figures, we prefix to them a cypher to complete that number. Divide 1.728 by .012 .012)1.728(144 52 48 Because Because the number of decimal figures in the divisor and dividend, are alike; the quotient will be integers. Divide 2.00000 by 3.1416 3.1416)2.00000(.636618 115040 207920 194240 57440 260240 8912 There being 4 decimal figures in the divisor, and 10 including the cyphers brought down in the dividend, the difference, which is 6 figures, to be cut off in the quotient. Divide 87446071 by .004387. Answer 199.33. Answer .001296. Answer 2.44502. PROB. I. To reduce a Vulgar Fraction to a Decimal one of the same Value. Having annexed a sufficient number of cyphers as decimals, to the numerator of the vulgar fraction, divide by the denominator ; and the quotient thence arising, will be the decimal fraction required. EXAM EXAMPLE S. Reduce to a decimal fraction. 4)3.00(-75 Answer. 20 For of one shilling, yard, perch, &c. is equal to one fourth of three shillings, yards, perches, &c. therefore if 3 be divided by 4, the quotient will be The answer. Reduce to a decimal fraction. 5)2.0(.4 Answer: Reduce to a decimal fraction. 25.)12.00(48 Answer. 200 Reduce to a decimal fraction: Answer .1146789. PROB. II. To find the Value of a decimal Fraction, in the known Parts of the Integer. Multiply the decimal proposed, into the number of equal parts contained in the integer, and the product will be the number of such parts as are expressed by the fraction. What is the value of .25 of a pound sterling ? |