Note. 13 cwt. 1 qr. 15 lb. 134 cwt.-13.383-+-cwt. This multiplied by $4.27 gives $57.14541. Observe, that there must be as many decimal places in the product as in the multiplicand and multiplier together. In this instance there are five places. It is not necessary to notice any thing smaller than mills in the result, therefore $57.145 will be sufficiently exact for the answer. 5. What cost 12 cwt. 0 qrs. 19 lb. of rice, at $3.28 per cwt. ? 6. What cost 13 cwt. 2 qrs. 4 lb. of hops, at $5.75 per cwt. 7. What cost 3 hhds. 43 gal. of wine, at $98 per hhd. ? Note. 3 hhds. 43 gal. is 343 hhds.; this reduced to a decimal is 3.683 hhds., nearly. 8. What cost 17 hhds. 18 gal. of molasses, at $23.25 per hhd. ? 9. What cost 13 hhds. 53 gal. of gin, at $47.375 per hhd. ? 10. What cost 4 hhds. 27 gal. 3 qts. of brandy, at $108.42 per hhd.? 11. Express in decimals of an cwt. the quarters, pounds, and ounces in the following numbers:-3 cwt. 2 qrs. 22 lb. ; 17 cwt. 1 qr. 11 lb. 5 oz. ; 4 cwt. 0 qr. 16 lb. 3 oz. 12. Express in decimals of a hogshead the gallons, quarts, pints, &c. in the following numbers :-43 hhds. 17 gal. 2 qts; 14 gal. 6 qts. 1 pt. ; 7 hhds. 0 gal. 3 qts. 1 pt. 13. What cost 8 gal. 3 qts. 1 pt. of gin, at $0.43 per gal. ? 14. What cost 17 lb. 13 oz. of sugar, at $0.12 per lb. ? 15. What cost 231b. 7 oz. of sugar, at $11.43 per cwt. ? 16. What cost 11 gals. 2 qts. of brandy, at the rate of $98.48 per hhd. ? 17. What cost 17 yds. 3 qrs. 2 nls. of broadcloth, at $7.25 per yard? 18. What cost 2 qrs. 3 nls. of broadcloth, at $6.42 per yard? Express the fractions in the following examples in deci mals. 19. What part of 1 yd. is 3 qrs. 2 nls. ? 23. What part of 1 qr. is 13 lb. 5 oz. ? 24. What part of a day is 6 hours? 25. What part of a day is 16 h. 25 min. ? 26. What part of a day is 13 h. 42 min. 11 sec. ? 28. What part of an hour is 38 min. 47 sec. 1 30. What part of 1 ft. is 2 in. ? 31 What part of 1 ft. is 7 in. ? 32. What part of a rod is 7 ft. 4 in. ? 33. What part of a mile is 7 rods, 13 ft. ? 36. What part of 1£. is 11s. 5d. 3 qr.? 37. At 2£. 5s. per cwt., what cost 5 cwt. 3 qrs. of raisins ? Note. 2£. 5s.—2.25£., and 5 cwt. 3 qrs.=5.75 cwt. Multiplying these together, the result is 12.9375.£. The decimal part of this result may be changed to shillings and pence again. .9375£. is .9375 of 20 shillings; therefore if we multiply 20 shillings by .9375, or, which is the same thing, if we multiply .9375 by 20, we shall obtain the answer in shillings and parts of a shilling. This is evident also from another course of reasoning. .9375£. is now in pounds; if it be multiplied by 20 it will be reduced to shillings. .9375 18.7500 The result is 18 shillings and .75 of a shilling, which may in like manrer be reduced to pence by multiplying it by 12. .75 12 9.00 is 12£. 18s. 9d. The result is 9d. The answer, therefore, 38. What cost 3 cwt. 2 qrs. 7 lb. of hops, at 2£. 3s. 6d. per cwt. ? 39. What cost 17 yds. 2 qrs. 2 nls. of broadcloth, at 2£. 5s. 7d. per yard? 40. What cost 8 cwt. 1 qr. 13 lb. of wool, at 3£. 7s. 6d. per cwt. ? 41. What cost 3 hhds. 43 gals. of wine, at 32£. 14s. 8d. per hhd. ? 42. How many cwt. of raisins in 73 casks, each cask containing 2 cwt. 0 qrs. 25 lbs? Note. 737.6 and 2 cwt. 0. qrs. 25 lb.-2.2232+ cwt. These multiplied together produce 16.8957 cwt. The fractional part of this may be changed to quarters, pounds, &c. as the fractions in the last examples were changed to shillings and pence. .8957 cwt. is .8957 of 4 quarters, or it is bundred-weights and may be reduced to quarters and pounds by multiplying by 4, and by 28. The answer is 16 cwt. 3 qrs. 16 lb. 5 oz. nearly. The same result may be obtained by changing the decimal .8957 cwt. to a common fraction, and proceeding according to the method given in Art. XVI. 43. How many cwt. of cotton in 5% bales, each bale containing 4 cwt. 3 qrs. 7 lb. ? 44. How many cwt. of coffee in 132 bags, each bag containing 1 cwt. 3 qrs. 15 lb. ? 45. Find the value of .387£. in shillings, pence, and farthings. 46. Find the value of .9842£. in shillings, pence, and farthings. 47. Find the value of .583 cwt. in quarters, pounds, &c. 48. Find the value of .23 cwt. in quarters, pounds, &c. 49. Find the value of .73648 cwt. in quarters, pounds, Szc. 50. Find the value of .764s. in pence and farthings. 51. Find the value of .3846 qr. in pounds and ounces. 52. Reduce 3.327 qrs. to pounds. 53. Reduce 4.684£. to pence. 54. Find the value of .346 of a day in hours, minutes, &c. 55. Find the value of .5876 of an hour in minutes and seconds. 56. Express in decimals of a foot the inches in the following numbers :-3 ft. 6 in.; 4 ft. 3 in.; 7 ft. 9 in.; 3 ft. 8 in.; 5 ft. 7 in.; 9 ft. 10 in. 57. Find the value of .375 ft. in inches and parts. 58. Find the value of .468 of a square foot in square inches. 59. Find the value of .8438 of a solid foot in solid inches. 60. How many square feet in a board 9 in. wide and 15 ft. 3 in. long. Change the inches to decimals of a foot. Since the answer will be in square feet, it will be necessary to find the value of the decimal in square inches. In genera! however, it will be quite as convenient to let the answer remain in decimals. The answer is 11.4375 ft. It will be sufficiently exact to call it 11.4 ft. 61. How many square feet in a floor 14 ft. 7 in. wide and 19 ft. 4 in. long? X 62. How many square feet in a board 1 ft. 8 in. wide and 17 ft. 10 in. long. 63. How many solid feet in a stick of timber 28 ft. 4 in. long. 1 ft. 2 in. wide, and 11 in. deep? Note. In questions of this kind it will generally be most convenient to change the inches to decimals of a foot, because when the whole is reduced to inches, the numbers become very large and the operation becomes tedious. Tenths, generally, and hundredths in almost every case, will be sufficiently exact for common purposes. Those who measure timber, boards, wood, &c. would find it extremely convenient to have their rules divided into tenths of a foot, instead of inches. There is a method of performing examples of this kind called duodecimals, which will be explained hereafter, but it is not so convenient as decimals. 64. How many solid feet in a pile of wood 4 ft. 2 in. wide, 3 ft. 8 in. high, and 13 ft. 4 in. long? It has been already remarked that in interest discount. commissions, &c. 6 per cent., 7 per cent., &c. signifies 1, &c. of the sum. This may be written as a decimal fraction. In fact this is the most proper and the most convenient way to express, and to use it. 1 per cent. is .01; 2 per cent. is .02; 6 per cent. is .06; 15 per cent. is .15; 6 per cent. is .065, &c. This manner of expressing the rate will be very simple in practice, if care be taken to point the decimals right in the result. 65. A commission merchant sold a quantity of goods amounting to $583.47, for which he was to receive a commission of 4 How much was the amount of the commission? per cent. 583.47 .04 $23.3388 Ans. There are two decimal places in each factor, consequently there must be four places in the result. The answer is $23.34 nearly. 66. What is the commission on $1358.27, at 7 per cent. ? 67. What is the commission on $1783.425, at 5 per cent.? 68. A merchant bought a quantity of goods for $387.48, and sold them so as to gain 15 per cent. How much did he gain, and for how much did he sell the goods? 69. What is the insurance of a ship and cargo, worth $53250, at 21 per cent.? Note. 2 per cent is equal to .025, for 2 per cent. is .02, and per cent. is 1⁄2 of an hundredth, which is 5 thousandths. 70. What is the duty on a quantity of books, of which the invoice is $157.37, at 15 per cent. ? or 10 10 per Note. It is usual at the custom-house to add per cent. to the invoice before casting the duties. cent. on $157.37 is $15.737, which, added to $157.37 makes $173.107. The duties must be reckoned on $173.107. When the duties are stated at 15 per cent. they will actually be 161 per cent. on the invoice; because 15 per cent. on will amount to 1 per cent. on the whole. It will be most convenient generally to reckon the duties at 16 per cent., instead of adding of the sum and then reckoning them at 15 per cent. When the duties are at any other rate, the rate may be increased of itself, instead of increasing |