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 12)7.0000 to a decimal. By annexing four ciphers, we obtain four decimal figures. We might, .5833+ however, annex more ciphers, and carry the decimal still lower. 48. Change to a decimal. 49. Change the following fractions to their respective decimals... 2. 13. 1. 12. 37. 375. 6 5 14 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 £31615 to a decimal expression. CHANGE OF COMPOUND NUMBERS TO DECIMALS. To reduce the lower denominations of a compound number to the decimal of a higher denomination. RULE. Reduce the given quantity to a common fraction, then change this fraction to a decimal. See page 171. 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. CHANGE OF DECIMALS TO COMPOUND NUMBERS. To reduce the decimal, of a higher denomination, to its value in whole numbers of lower denomination. RULE. 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 thus with the decimal in each succeeding product. .6526 20 13.0520 64. Reduce .6526 of a £ to its value in shillings, &c. 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.+ 12 .6240 4 2.4960 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, of a dollar is called a shilling. In Pennsylvania, New Jersey, Delaware, and Maryland, of a dollar is called a shilling. In South Carolina and Georgia, called a shilling. of a dollar is In Canada, of a dollar is called a shilling. In Great Britain, the shilling, of the Sterling currency, is equal to of a dollar 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? 6) 1.000 6) 2.000 .1663 .333 of the number expressing shillings, expresses an equal value in decimals of a dollar 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.? 75. How many cents and mills in a Canada shilling› in 2s.? in 3s.? in 4s.? in .5s.? 76. How many cents and mills in a shilling, Sterling, of Great Britain? in 2s.? in 3s.? in 4s.? To change the currencies of pounds, shillings and pence, of every variety of value, to Federal money. RULE. Reduce the pounds, if there be any, to shillings Denote the shillings as units, reduce the pence and farthings to the decimal of a shilling, and multiply the sum by that fraction of a dollar which is equal to one shilling. 77. Change 13s. 6d., of the old currency of New England, to Federal money. 13s. 6d. 13.5s. 13.5 x 2.25. 78. Change £42 19s. 4 d., of the old currency of New England, to Federal money. £42 19s. 4 d. = 859.375s. 79. Change 13s. 6d., of the old currency of New York, to Federal money. 80. Change £25 17s. 8 d., of the old currency of New York, to Federal money. 81. Change 18s. 11d., of the old currency of Pennsyl vania, to Federal money. 82. Change 14 7s. 6 d., of the old currency of Pennsylvania, to Federal money. 83. Change 16s. 10d., of the old currency of Georgia, to Federal money. 84. Change £54 12s. 114 d., of the old currency of Georgia, to Federal money. 85. Change £21 9s. 3 d., of the currency of Canada, to Federal money. 86. Change £5 12s. 4d. Sterling, Great Britain, to Federal money. III. PERCENTAGE. PERCENTAGE has already been explained in page 163. 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. 1. A merchant having $1426 in the bank, drew out 5 per cent. of it. What sum did he draw? 1426 .05 $71.30 Since 5 per cent. of any quantity is 15 of 2. What is 1 per cent. of $100? of $834? 6. What is 24 per cent. of 1852 dollars? When the rate is a fraction of 1 per cent. First, re duce the rate to a decimal, by multiplying .01 by the frac tion. Then multiply by the decimal rate as before. 7. What is 3 per cent. of 234 dollars? 10. What is 2 11. What is 64 12. What is 10 13. Find 7 per cent. of 344 dolls. When there is a fraction in the 344-100=3.44 rate per cent. which cannot be ex actly expressed by a decimal as in this example-we first find 1 per cent. of the given sum, by dividing it by 100, and then multiply this 73 2408 114 $25.223 quotient by the mixed number that expresses the rate. 14. What is 4 per cent. of 624 dollars? 24.32 .07 $1.7024 18. What is 7 per cent. of 24 dolls. 32 cts.? Here we have cents [decimals] in the number on which the percentage is to be taken. We however multiply as usual in decimals, and the first two decimal figures in the product express cents, the third mills, the fourth tenths of a mill. 19. What is 14 per ent. of $641.94 ? 20. What is 4 per cent. of $37.26? 21. What is 11 per cent. of $150.75 ? To find what per cent. a smaller number is of a larger,Consider the smaller number as a numerator, and the larger as a denominator of a fraction; then reduce this fraction to a decimal. See page 188. 22. If a man, having $94 deposited in bank, draw out $25, what per cent. of his deposit does he draw? 25 is 2 of 94. Then 3.26. Ans. 26 29 per cent. 23. What per cent. of 240 dollars is 32 dollars? 24. What per cent. of 12 dollars is 7 dollars? 25. What per cent. of $95.21 (9521 cts.), is $4.22 ? To find a percentage of a compound number,—Multiply by the rate per cent., as a whole, or mixed number, and divide the product by 100, or the factors of 100. 26. What is 6 per cent. of £22 10s. 9d.? 27. What is 4 per cent. of £41 15s. 6d. ? 28. What is 3 per cent. of £8 16s. 8d.? |