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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 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 operaticn 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 st. 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 in

&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.; 62 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 per cent. How much was the amount of the commission ?

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 823.34 nearly.

66. What is the commission on $1358.27, at 7 per cent.my 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 į per cent. is į 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. ?

Note. It is usual at the custom-house to add to or 10 per cent to the invoice before casting the duties.10 per 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 16į per cent. on the invoice; because 15 per cent. on jó will amount to lì per cent on the whole. It will be most convenient generally to reckon the duties at 16per cent., instead of adding to of the sum and then reckoning them at 15 per cent. When the duties are at any other rate, the rate may be increased to of itself, instead of increasing

the invoice lo. For instance, if the rate is 10 per cent. call it 11 per cent., if the rate is 14 per cent. call it 15% per cent., then the multiplier will be .154. If the rate is 12, per cent., that is, .125, io of this is .0125, which added to 1125 makes .1375 for the multiplier.

71. Whạt is the duty on a quantity of tea, of which the inyoice is $215.17, at 50 per cent. ?

72. What is the duty on a quantity of wine, of which the invoice is $873, at 40 per cent. ?

73. What is the duty on a quantity of saltpetre, of which the invoice is $1157, at 7į per cent. ?

74. Imported a quantity of hemp, the invoice of which was $1850, the duties 131 per cent.

What did the hemp amount to after the duties were paid ?

75. Bought a quantity of goods for $58.43, but for cash the seller made a discount of 20 per cent. What did the goods amount to after the discount was made ?

76. A merchant bought a quantity of sugar for $183.58, but being damaged he sold it so as to lose 71 per cent. How much did he sell it for ?

77. Bought a book for $.75, but for cash a discount of 20 per cent. was made. What did the book cost ?

78. Bought a book for $4.375, but for cash a discount of 15 per cent. was made. How much did the book cost ?

79. What is the interest of $43.25 for 1 year, at 6 per cent. ?

80. What is the interest of $183.58 for 1 year at 7 per cent. ?

81. At 6 per cent. for 1 year, what would be the rate per cent. for 2 years ? For 3 years ? For 4 years ?

82. At 6 per cent. for 1 year, what would be the rate per cent. for 6 months ? For 2 months : For 4 months ? For 1 month ? For 3 months ? For 5 months ? For months ? For 8 months ? For 9 months ? For 10 months ? For 11 months ?

83. At 6 per cent. for 1 year, what would be the rate per cent. for 13 months ? For 14 months ? For 1 year and 5 months ?

84. If the rate for 60 days is 1 per cent., or .01, what is the rate for 6 days ? For 12 days ? For 18 days ? For 24 days ? For 36 days! For 42 days ? For 48 days ? For 51 days!

Note. The interest of 6 days is l_ per cent., that is .001. The interest of 1 day therefore will be of io, or fb per cent., or .00016. The rate for 2 days twice as much, &c. In fact the rate for the days may always be found by dividing the number of days by 6, annexing zeros if necessary, and placing the first figure in the place of thousandths, if the number of days exceeds 6.

85. What is the interest of $47.23 for 2 months, at 6 per cent. ?

Note. When the rate per cent. is stated without mentioning the time, it is to be understood for 1 year, as in the following examples.

86. What is the interest of $27.19 for 4 months, at 6 per cent. ?

87. What is the interest of $147.96 for 6 months, at 6 per cent. ?

88. What is the interest of $87.875 for 8 months, at 6 per cent. ?

89. What is the interest of $243.23 for 14 months, at 6 per cent. ?

90. What is the interest of $284.85 for 3 months, at 6 per cent. ?

91. What is the interest of $28.14 for 5 months, at 6 per cent. ?

92. What is the interest of $12.18 for 7 months, at 6 per cent. ?

93. What is the interest of $4.38 for 9 months, at 6 per cent. ?

94. What is the interest of $15.125 for 11 months, at 6 per cent. ?

95. What is the interest of $127.47 for 2 months and 12 days, at 6 per cent. ?

96. What is the interest of $373.62 for 4 months and 24 days, at 6 per cent. ?

97. What is the interest of $115.42 for 7 months and 15 days, at 6 per cent. ?

98. What is the interest of $516.20 for 11 months and 23 days, at 6 per cent. ?

99. What is the interest of $143.18 for 1 year, 7 months, and 14 days, at 6 per cent. ?

100. A gave B a note for $357.68 on the 13th Nov. 819, and paid it on the 11th April, 1822, interest at 6

per cent. How much was the principal and interest together at the time of payment ?

101. A note for $843.43 was given 5th July, 1817, and paid 14th April, 1822, interest at 6 per cent. How much did the principal and interest amount to?

102. A note was given 7th March, 1818, for $587; a payment was made 19th May, 1819, of $ 53, and the rest was paid 11th Jan. 1820. 'What was the interest on the note ?

103. What is the interest of $157 for 2 years, at 5 per cent. ?

104. What is the interest of 13£. 3s. 6d. for 1 year, at 6 per cent. ?

Note. If the shillings be reduced to a decimal of a pound, the operation will be as simple as on Federal money. The following is a more simple method of changing shillings to decimals, than the one given above. to part of 20s. is 2s., therefore erery 2s. is to £. or .1£. Every shilling is 26., that is ook. or .05£. ; 3s. then is .1.. and .05£., or.15£.

In 1£. there are 960 farthings. I farthing then is glo of 1£. 6d. is 24 farthings, consequently to of a £. These are rather larger than thousandths, but they are so near thousandths that in small numbers they may be used as thou-sandths. *£.=1.£. when reduced, and 1864.=.o., so that 24 farthings are exactly 1ă67£. or .025£. If the number of farthings is 13 they will be li£. and rather more than į of another thousandth. This may be called Toto or .014, and the error will be less than į of idüo If the number of farthings be less than 12 they may be called so many thousandths, and the error will be less than { of lobo: If the number of farthings is between 12 and 36 add i to them, if more than 36 add 2, and call them so many thousandths ; and the result will be correct within less than } of tood. 48 farthings make 1 shilling, therefore there will never be occasion to use more than this number. From the above observations we obtain the following rule. Call cvery two shillings one tenth of a pound, every odd shilling five hundredths, and the number of farthings in the pence and farthings so many thousandths, adding one if the number is between twelve and thirty-six, and two if more than thirty-sit.

It will be well to remember this rule, because it will be

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