12. How many times is 800 ccm. contained in 50 1.? 13. How many times is 450 ccm. contained in 22.5 hl.?

14. A dime weighs 2.5 g. How many dimes can be coined from 3 kg. standard silver? how many 25 pieces, weights being in proportion to values?

15. How many times is 1521 mg. contained in 5.9319 kg.? Example. Find the area of a rectangle, if its length is 425.8 m. and its breadth is .3256 km.

SOLUTION.

First, reduce .3256 km. to meters.

.3256 km. = 325.6 m.

Second, multiply in the usual manner and get for product 138,640.48 qm. Reduce this to ares by dividing by 100, and reduce the ares to hectares by dividing by 100. Both operations can be performed at once by moving the decimal point four places to the left. Ans. 13.864048 ha.

425.8

325.6

25548

21290

8516

12774 138640.48 qm.

EXERCISE 165

Find the area of each of the following rectangles :

7. Find the

solid whose

volume of a rectangular dimensions are 1.2 m., 9 m., and .75 m.

8. Find the area of a triangle whose sides are 14 m., 48 m., and 50 m.

9. Find the area of a circle whose radius is .78 m.

10. Find the volume of a sphere whose radius is 18 cm.

11. The legs of a right triangle are 56 cm. and 105 cm. Find the hypothenuse.

12. Find the volume of a rectangular prism, the base being 14 m. by 12 m., and height 9.5 m.

13. A boiler has 300 tubes 2.4 m. long, 7.5 cm. diameter. What is the area of the tube heating surface?

14. Find the weight of a spherical cast iron shell 32.5 cm. outside and 27.5 cm. inside diameter.

15. An iron plate 3 mm. thick weighs 1 kg. What is its area?

The following approximations should be fixed in mind : 1 meter = 39 inches; 1 kilometer = of 1 mile. 1 centimeter = of an inch; 1 hectare = 2 acres. 1 liter = 1 quart; 1 kilogram = 2 pounds Avoirdupois.

1 liter

1 hectoliter

= .3861 sq. mi.

cu. centimeter = .061 cu. in.

= 2.83774 bu.

1 kilogram

= 2.20462 lb.

1 tonneau, or ton = 2204.6 lb.

*Liquid quarts, or 0.9081 dry quarts.

MISCELLANEOUS EXAMPLES

(ARRANGED BY TOPICS)

NOTATION

1. Write in figures ten million ten.

2. Write in figures seven million two hundred five thousand.

3. Write in figures one billion one million one.

4. Write in figures five million fifty thousand.

5. Write in figures ten billion ten million one hundred. 6. Write decimally: Twenty-five tenths. One hundred twenty hundredths. One hundred and fifty-five hundredths. Ten thousand ten, hundred thousandths. One million one, ten-millionths. Fifty-five thousand two hundred eighteen ten-thousandths. Twelve millionths.

ADDITION AND SUBTRACTION

7. The following table of railroad mileage in the United States is taken from the report of the Interstate Commerce Commission:

Find the number of miles built during each year, begin

ning with 1890, up to 1905.

11. Multiply 10,500 by 60,600. 12. Multiply 15,010 by 50,080. 13. Multiply 1.01 by 7.07.

14. Multiply 9010.9 by 90.4.

15. A train travels at the rate of 30.25 mi. an hour. How far will it go in 5 hr?

16. Find the price of 871 A. of land at $43.75 an acre. 17. Find the price of 4225 hu. of wheat at 841¢ per bushel.

18. Find the value of .1 x.2 x .3 x .4 x .5 x .6 x .7. 19. Find the value of (1.03).

20. The number of bales of cotton produced in Texas in 1901-2 was 2,993,000, and in 1900-01, 3,550,000. Allowing 500 lb. to a bale, how many more pounds of cotton were produced in the latter year than in the former?

DIVISION

21. A steamer's cargo consisted of 120,000 bu. of corn, valued at $57,000; 13,541 bbl. of flour, valued at $47,499; 3050 bales of cotton, valued at $158,224. Find the value of a bushel of corn, a barrel of flour, and a bale of cotton. 22. Divide 26.78508 by .072.

23. The annual consumption of sugar in a certain state was, in 1890, 702,201 T., which was found to be 49.93 lb. per head of population. Find the population.

24. Make a column of eight numbers, the first of which is 73,214, the second is of the first, the third is of the second, and so on for the other numbers.

25. How many miles in 278,784,000 ft. ?

26. Divide 1.1252 - (.784)2 by 1.125.784.

27. Divide (.75)3 — (.26)3 by .75 — .26.

28. Divide 14.302 by 83.92, correct to four places.

29. Divide 24.619 by 56,000.

30. The length of a degree on the earth's surface is approximately 69.15 mi. Two places are on the same merid

ian and 1000 mi. apart.

in latitude.

Find, in degrees, the difference

=

31. Two places on the 60th parallel of latitude are 300 mi. apart. Find the difference of their longitudes. (1o = 183,085. ft.)

32. A bankrupt's liabilities are $ 47,875; his assets are $38,650. How many cents on the dollar can he pay?

33. The product of two numbers is 642,978, and one of the numbers is 5.67. Find the other number.

34. If the quotient is 24,400, the remainder is 15, and the dividend is 6,100,015, find the divisor.