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36. Divide 64.395 by 40.5. Divide 5.8674 by 127

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38. How many times is .27 contained in 1.224 ?

.27)1.224(4.533+ more, here shows, that the true

108

144

135

90

81

90

81

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The sign of addition, or

quotient is more than the pre

ceding figures express. We might continually annex ciphers to this remainder, and carry on the division, but we should never arrive at a complete quotient. For the purposes of business, it is seldom necessary to extend the quotient below thousandths.

39. How many times is 1.23 contained in 3021.741 ? 40. How many times is 1243.4 contained in 5.37148? 41. How many times is .204 contained in 77112? 42. How many times is 4.2 contained in 194.334? / 43. How many times is 30.02 contained in 94.657 ? 44. How many times is .44 contained in .1606 ? 45. What is the quotient of 42.65 divided by 36? 46. What is the quotient of .8 divided by 8?

CHANGE OF COMMON FRACTIONS TO DECIMALS.

RULE. Annex ciphers to the numerator, and divide it by the denominator: the quotient will be the decimal. 47. Change to a decimal.

12)70000
.5833+

By annexing four ciphers, we obtain four decimal figures. We might, however, annex more ciphers, and carry the decimal lower.

48. Change to a decimal.

49. Change the following fractions to their respective decimals... 1. 13. 18. 12. 37. 375.

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26

50. Change of a dollar to a decimal; that is, find how many cents and mills there are in of a dollar. 51. Change $48 to a decimal expression.

52. Change £31614 to a decimal expression.

When the lower denominations of a compound number are to be reduced to the decimal of a higher denomination,- First reduce the given quantity to a common fraction, (as taught in Sec. 27,) then change the common fraction to a decimal.

53. Reduce 7s. 6d. to the decimal of a £.

54. Reduce 15 shillings to the decimal of a £. 55. Reduce 6d. 3qr. to the decimal of a shilling. 56. Reduce 2s. 11d. 3qr. to the decimal of a £. 57. Reduce 1 farthing to the decimal of a shilling. 58. Reduce £18 2s. 7d. to a decimal expression. 59. Reduce 14dwt. 18gr. to the decimal of an oz. Troy. 60. Reduce 4qt. 1pt. to the decimal of a bushel. 61. Reduce 3qt. 1pt. 2gl. to the decimal of a gallon. 62. Reduce 10r. 3yd. 2ft. to the decimal of a mile? 63. Express 29yd. 2qr. 3na. of cloth decimally, and find its cost, at $7.625 per yard.

To reduce the decimal of a higher denomination to its value in whole numbers of lower denomination,— Multiply the decimal by that number of the next lower denomination which makes a unit of the higher, and the product will be of the lower denomination. Proceed in like manner with the decimal in each succeeding product.

64. Reduce .6526 of a £ to its value in shillings, &c

.6526
20

13.0520

12

.6240

4

2.4960

We multiply the decimal of a £ by 20, to find the shillings, because, there are 20 times more shillings than pounds in any sum, whether the sum be a whole number or a decimal. The same reasoning also applies, in finding the pence, and the farthings. Answer, 13s. Od. 2qr. +

65. Reduce .4039 of a £ to its value in shillings, &c. 66. Reduce .857 of a shilling to pence and farthings. 67. Reduce .76 of a ton to cwt. qr. lb. &c. 68. In .2094 of a day, how many hours, minutes, &c.? 69. In .57 of an acre, how many roods, rods, &c.? 70. Reduce £15.2908 to its proper expression in pounds, shillings, pence, and farthings.

EXCHANGE OF CURRENCIES.

In New England, Virginia, Kentucky, and Tennessee, of a dollar is called a shilling.

In New York and North Carolina, called a shilling.

of a dollar is

In Pennsylvania, New Jersey, Delaware, and Maryland, of a dollar is called a shilling.

In South Carolina and Georgia, of a dollar is called a shilling.

71. How many cents and mills, that is, what decimal of a dollar, in a New-England shilling? in 2 shillings? in 3 shillings? in 4 shillings? in 5 shillings?

72. How many cents and mills in a New-York shilling? in 2s.? in 3s.? in 4s.? in 5s.? in 6s.? in 7s.? 73. How many cents and mills in a Pennsylvania shilling? in 2s.? in 3s.? in 4s.? in 5s.? in 6s.?

74. How many cents and mills in a Georgia shilling? in 2s.? in 3s.? in 4s.?

To change shillings, pence, and farthings to Federal money,- Reduce the pence and farthings to the decimal of a shilling, and multiply the whole sum by that fracion of a dollar which is equal to one shilling.

75. Change 14s. 6d. 3qr., of the currency of New England, to Federal money.

76. Change 12s. 8d. 1qr., of the currency of NewYork, to Federal money.

77. Change 16s. 5d., of the currency of Pennsylvania, to Federal money.

78. Change 18s. 8d. 2qr., of the currency of Georgia, to Federal money.

79. What is the value, in Federal money, of 8 NewEngland shillings? 8 New-York shillings? 8 Pennsylvania shillings? 8 Georgia shillings?

PERCENTAGE AND INTEREST BY DECIMALS.

Percentage and Interest have already been explained in pages 163, and 165. Since PER CENT. indicates hundredths, it is properly expressed in the first and second decimal places, taken together. Thus, 6 per cent. is .06; 12 per cent. is .12. A fraction of 1 per cent. is expressed in decimals lower than hundredths. Thus, per cent. is .005; per cent. is .0025; 6 per cent. is .065; 12 per cent. is .1275.

Multiplying by a decimal, produces such a part of the multiplicand, as the decimal indicates. Therefore,

To find the percentage on any sum,- Multiply the sum by the decimal which denotes the rate per cent.

80. An auctioneer sold a bale of goods for $648.85, on which he received a commission of 2 per cent. What did his commission amount to?

81. Suppose an insurance office to charge 12 per cent. for a fire risk; what will it cost to insure a house, which is valued at $4500?

82. Suppose the shares in a rail-road stock, to cost originally $100 apiece; what is the value of 15 shares, after the stock has risen 12 per cent.?

83. A smith bought 7 tons of iron, at $95 per ton; and for cash, obtained a discount [abatement] of 5 per cent. How much did he pay?

84. What is the amount of $85.62, at 6 per cent. interest, for 3 years, 5 months, and 17 days?

85. What is the interest of $225, from September 21, 1831, to February 7, 1834, at 6 per cent.?

A part of a debt is sometimes paid, and the remainder still continues at interest. In such case, it is usual to compute the interest to the time of the partial payment, subtract the payment from the amount, and consider the remainder as the future principal.

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86. A note of $58.25 has been standing 18 months at 6 per cent.; but, 5 months after the date, $14 were paid and endorsed. What is the amount of the note? 87. A note of $120, at 6 per cent., is dated, July 5, 1830; and on the back of it is this endorsement,― June 24, 1831, Received, $56. What amount is required to pay this note, on the 21st. of March, 1833?

88. Suppose a note of $432.50, at 6 per cent., to be dated January 10, 1832, on the back of which, is this endorsement, October 7, 1833, Received, $200;what is the amount of this note, May 9, 1834?

-

Interest is sometimes computed for each year separately, and the amount of each year is taken for the principal of the succeeding year. The interest thus obtained, is called Compound interest.

89. Suppose a note of $1528, to be dated August 12, 1827, and to remain at 6 per cent. compound interest, until April 9, 1835; what is the amount?

90. A man owing $2534, due in 4 years, without interest, wishes to advance payment. What difference will it make to him, whether 6 per cent. interest for the time be allowed as discount, or, the discount be computed according to the just rule, in page 168?

THE END OF PART SECOND.

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