67. If the length of Jupiter's day is 9 hr. 56 min., how many more days has Jupiter than the earth in one year?

68. If $500 can be counted in one minute, how long will it take to count $1000000 ?

69. What is the difference between the daily income of a man whose salary is $1200 a year and of one whose salary is $1600 ?

70. Counting 12 hr. a day, how long would it take to count a billion at the rate of 750 a minute?

71. How many days old was a person Oct. 5, 1904, who was born July 27, 1861 ?

72. The ancient Roman mile is 0.917 of the English mile. Express the diameter of the earth (7926 English miles) in Roman miles.

73. The diameter of a fly wheel is found by measurement to be 20.12 in. Find its circumference.

74. The specific gravity of copper is 8.97; of gold, 19.36; of lead, 11.36. Find the weight of a lump of each equal in bulk to a liter of water.

75. The diameter of the earth is 7926 mi. The sun's diameter is 111.454 times the earth's diameter. sun's diameter correct to miles.

Find the

76. A lump of iron containing 12 cu. ft. is drawn out into a rod 50 ft. long. What is the diameter of the rod?

77. The true length of the year is 365.2426 da. What error is made by calculating the year as 365 da., and adding a day every leap year, omitting three leap years in four centuries?

78. The edge of a cube is 12 in. What is the edge of a cube three times its volume ?

79. How many miles an hour does a person walk who takes two steps a second and 1900 steps to the mile?

80. Express in words 0.12071 and 12000.00071.

81. How many steps 0.8 of a meter long will a person take in walking 10Km?

82. A clock which gains one minute in 10 hr. is correct on Monday noon. What is the correct time when it indicates Monday noon of the next week?

In scientific work, when numbers depend upon measurements and therefore cannot be expressed with absolute accuracy the index notation is frequently used. Thus, the wave length of blue light, determined by the physicist to be 0.000431mm would usually be written 4.31 x 10-4 mm. The distance from the sun to the earth is determined by the astronomer to be approximately 93000000 mi. In index notation it would be written 9.3 x 107 mi.

83. Express the following in the index notation:

0.0000025; 36500000000; 20000000; 41100000.

84. Express in the common notation 1.1 x 10-5; 3.6×106; 4.321 x 10-8; 5 × 10-4; 5 × 106.

85. From 3542 subtract 21316.

86. Find the sum of 34.612, 121.5112, and 25.1112 and express it in the decimal notation.

87. If brass weighs 525 lb. per cubic foot, find the weight of a circular brass plate 21 in. in diameter and in. thick.

88. If a cubic foot of gold may be made to cover uniformly 432000000 sq. in., find the thickness of the gold.

89. If a gallon of water contains 277.274 cu. in., and a cubic foot of water weighs 1000 oz., how much does a pint of water weigh? How many gallons will weigh a ton?

90. Four circles each 1 ft. in diameter are so placed that two of them touch two of the others, and the remaining two both touch three of the others; find the area of the figure whose angles are at the four centers.

91. What (standard) time is it in Boston when it is 4.30 P.M. in San Francisco?

92. A ship's clock is corrected at 1 o'clock each day. If the ship passes over 10° 30′ each day, what change must be made in the clock (a) if the ship is sailing from W. to E.; (b) from E. to W.?

93. Find the remainders (without dividing) after 471321 has been divided by all of the numbers (except 7) from 2 to 12 inclusive.

94. Show without dividing that 133056 is divisible by 792.

95. A ship's clock is corrected every day at 1 P.M.; how much must it be put back or forward at 1, if the ship has passed over 11° of longitude from east to west?

96. When it is noon (standard time) Wednesday, Dec. 7, at Chicago, what time and date is it at Rome? at Tokyo? 97. A meter is defined as 1 x 10-7 of the distance from the pole to the equator. Find the circumference of the earth in kilometers.

98. Find the circumference of the earth in miles if the meter is equal to 39.37079 in.

99. If 1 cu. ft. of water weighs 1000 oz., and platinum is 20.337 times as heavy as water, how many feet of platinum wire 3000 of an inch in diameter would weigh a grain?

233.

and

PERCENTAGE

15=0.50=50% = 50 per cent,

} = 333 = 0.33} = 33}% = 33} per cent.

100

These are different ways of denoting the same fractional part. In business operations it is customary to express fractions in hundredths, but in stating problems the denominator 100 is omitted and the per cent symbol, %, or the expression per cent is used. Percentage is therefore only an application of the decimal fraction and not a separate department of arithmetic.

234. The word percentage is derived from the Latin per centum, meaning by the hundredths.

235. The number denoting how many hundredths are taken is called the rate per cent. Thus, if 5% of a number is to be taken, 5 is called the rate per cent, and 5% the rate.

236. The following examples illustrate several closely related operations frequently used in business transactions. Ex. 1. What is 8% of $750?

Solution. 8% of $750 = 0.08 of $750 = $60.

Ex. 2. 12 is what per cent of 240?

Solution. Let

x%= the rate.

Then

x% of 240 = 12,

x % = 24% = 2% = 0.05 = 5%.

1. Express the following fractions in per cent, also is decimals, 4, 10, 8, 3, 3, 4, 18, 12.

5

9 1,

2. 3 is what per cent of 4? 8 is what per cent of 4? 18 is what per cent of 27? 25 is what per cent of 200? 7 is what per cent of 2?

3. The population of a town is 7250. What is the population five years later if it has increased 7% in that time?

4. A town of 11750 inhabitants decreases 12% in ten years. What is its population after this loss?

5. Express the following as decimals: %, 331%, 0.5%, 125%.

6. What is 1% of 75? 1% of 100? 0.4% of &? 3% of 45?

7. Write as per cent 11, 24, 1, 0.001, 10, 2, 0.25, 2.5, 0.163.

8. The attendance in a certain school increased in one year from 318 to 425; find the rate per cent of increase.

9. In a certain school there are 291 boys and 315 girls. What percentage of the attendance is boys and what percentage is girls?

10. In a certain town the total school enrollment is 962; of this 156 are in the high school. What percentage of the whole enrollment is in the high school?