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. O 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 23 lb. 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 decimals. 19. What part of 1 yd. is 3 qrs. 2 nls.? 20. What part of 1 yard is 1 qr. 3 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.? 27. What part of an hour is 47 min.? 28. What part of an hour is 38 min. 47 sec.? 29. What part of a rod is 13 ft.? 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.? 37. At 2£. 5s. per cwt., what cost 5 cwt. 3 raisins? qrs. of 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 20 18.7500 The result is 18 shillings and .75 of a shilling, which may in like manner be reduced to pence by multiplying it by 12. .75 12 9.00 The result is 9d. The answer, there fore, is 12. 18s. 9d. 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 gal. of wine, at 32£. 14s. Sd. per hhd.? 42. How many cwt. of raisins in 73 casks, each cask containing 2 cwt. O qrs. 25 lb. ? Note. 737.6 and 2 cwt. O qrs. 25 lb. = 2.223 cwt. These multiplied together produce 16.8948 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. .8948 ct. is .8948 of 4 quarters, or it is hundred-weights and may be reduced to quarters and pounds by multiplying by 4, and by 28. .8948 3.5792 28 46336 11584 The result is 3 qrs. and a fraction. Then multiply .5792 qrs. by 28, it gives 16 lb. and a fraction of a 16.2276 pound. Multiplying .2276 lb. by 16, it gives 3 oz. and a fraction of 16 13656 an ounce. 2276 3.6416 The answer is 16 cwt. 3 qrs. 16 lb. 31⁄2 oz. nearly. The same result may be obtained by changing the decimal .8948 cwt. to a common fraction, and proceeding according to the method given in Art. XVI. 43. How many cwt. of cotton in 53 bales, each bale containing 4 cwt. 3 qrs. 7 lb. ? 44. How many cwt. of coffee in 133 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, &r. 50. Find the value of .764s. in pence and farthings. 51. Find the value of .3846 qrs. in pounds and Ounces. 22. 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 general, 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? 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 st. 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, To, &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 2; 6 per cent. is .06; 15 per cent. is .15; 61 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 commision of 4 per cent. How much was the amount of the commission ? 583.47 $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 2 per cent.? Note. 21 per cent. is equal to .025, for 2 per cent. is .02, and per cent. is 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. ? |