The Complete Arithmetic, Oral and Written

952. To change the Metric to the Common System.

39.37 in., or 141732 in. =11811 ft. Therefore, 3.6 Km. are equal to 11811 ft.

RULE.-Reduce the metric number to the denomination of the principal unit of the table; then multiply by the equivalent, and reduce the product to the required denomination.

EXERCISES.

2. How many feet in 472 centimeters?

3. How many cubic feet in 2000 sters?

Ans. 15.485 ft.

4. How many gallons, liquid measure, in 325 deciliters?

5. How many gallons in 108.24 liters?
6. How many bushels in 3262 kiloliters?
7. How many acres in 436 ars?

Ans. 28 gal. 2.77 qt.

8. In 942325 centiliters, how many bushels? 9. In 456 kilograms, how many pounds? 10. In 42 ars, how many square rods? 11. Change 75.5 hektars to acres.

Ans. 10.774 A.

Ans. 1005.024 lb.

Ans. 186.56 A.

12. How many gallons in 243 liters of wine?

13. How many pounds of butter in 124 kilos?

19. What is the weight of 24 cu. dm. 148 cu. cm. of silver, if a

cu. centimeter weighs 11.4 g.?

Ans. 737.556 lb. Tr.

953. To change the Common to the Metric System.

1. In 10 lb. 4 oz. Troy, how many kilograms?

OPERATION.

10 lb. 4 oz. = 10.25 lb.

10.25 lb. x 5760 =59040 gr. 59040 gr.÷15.432 gr. = 3825.75 g.

3825.75 g. ÷ 1000 = 3.82575 Kg., Ans.

ANALYSIS.-The gram,

the principal unit of the table, is expressed grains; hence, reduce the pounds and ounces to grains. Since 15.432 gr. make 1 gram, there are

as many grams in 59040 gr. as 15.432 gr. is contained times in 59040 gr., or 3825.75 g. And since there are 1000 grams in a kilogram, dividing 3825.75 g. by 1000 g., the quotient is 3.82575. Therefore, there are 3.82575 Kg. in 10 lb. 4 oz.

RULE.—Reduce the given quantity to the denomination in which the equivalent of the principal unit of the metric table is expressed; divide by this equivalent, and reduce the quotient to the required denomination.

EXERCISES.

2. In 6172.9 lb av., how many kilograms? Ans. 2800.009 Kg. 3. How many ars in a square mile?

4. How many cu. decimeters in 1892 cu. feet?

5. In 892 gr., how many grams?

Ans. 57.8 g.

6. In 2 mi. 272 rd. 5 yd., how many kilometers? Ans. 4.59 Km.

7. How many sters in 264.4 cu. feet?

8. How many liters in 3 bu. 1 pk. ?

Ans. 114.5 1.

9. How many grams in 6 lb. Troy? In 6 lb. Avoir. ?

10. How many meters in 3 mi. 272 rd.?

11. In 1828 cu. yd. how many cu. meters? Ans. 1397.52 cu. m.

12. In 3588 sq. yards, how many sq. meters?

13. Bought 454 bu. of wheat, at $3 a bushel, and sold the same at $8.75 per hektoliter; how many hektoliters did I sell? Did I gain or lose, and how much? Ans. 160 Hl.; gain, $38.

14. In 13 gal. 3 qt. 2 pt. 3 gi., how many liters?

Ans. 53.35 1. + .

15. How many sq. meters of plastering in a room 18 ft. 6 in. long, 14 ft. wide, and 9 ft. 6 in. high? Ans. 55.367 sq. m.+.

TEST PROBLEMS.

954. 1. Find the weight of a barrel of flour (196 lb.) in Kg.? 2. What is the cost of a carpet for a room 10.5 m. long, and 8.4 m. wide, if the carpet is 84 cm. wide and costs $2.75 a meter?

Ans. $288.75.

3. A farmer sold 540 Hl. of wheat, at $2 a bushel, and invested

the proceeds in coal at $7 per tou.

How many tons did he buy?
Ans. 437.785 T.+.

4. What is the cost of a building lot 75 m. long and 62 m. wide, at $40 an ar?

Ans. $1860.

5. A bushel of wheat weighs 60 lb. What is the weight of 5 HI. of wheat, in kilograms? Ans. 386.05 Kg.

6. What will be the cost of a pile of wood 15.7 m. long, 3 m. high, and 7.52 m. wide, at $1.50 a ster?

7. The new silver dollar weighs 412 gr. Troy. How many grams does it weigh? Ans. 26.73 g.

8. How many acres of land in 24.6 Km. of a highway, which is 20 m. wide? Ans. 121.573 A.

What will

9. A bin is 4.2 m. long, 2.8 m. wide, and 1.5 m. deep. be the cost of filling it with charcoal, at 25 cts. a hektoliter?

10. A merchant bought 300 m. of silk in Lyons, at 12.5 francs a meter; he paid 75 cents a yard for duty and freight, and sold it in New York at $5 a yard. What was his gain? Ans. $670.61.

11. What price per pound is equivalent to $2.50 per Hg.?

12. If a man buys 5000 g. of jewels, at 35 francs a gram, and sells them at $15 a pennyweight, what was his gain or loss?

13. If a field produces 40 Hl. of oats to the hektar, how many bushels is that to the acre? Ans. 45.93 bu.

14. What price per peck is equivalent to 80 cts. a dekaliter? 15. What will be the cost of excavating a cellar 18.3 m. long, 10.73 m. wide, and 3.4 m. deep, at 20 cents per ster?

16. How many pounds Avoir. are there in 96.4 kilos of salt?

17. How many liters will a cistern hold that measures on the inside 5.5 ft. long, 4 ft. 6 in wide, and 4 ft. deep? Ans. 2803.383 1.

18. How many meters of lining that is 60 cm. wide will line 15 m. of silk that is 75 cm, wide? Ans. 18,75 cm.

19. A lady bought 40.5 m. of silk in Paris. What would be its value in Boston, at $4.75 per yard?

20. A bin is 4 m. long, 2.3 m. wide. contain 40 Hl. of grain?

How deep must it be to
Ans. 4.347 + dm.

21. How many sters of wood can be piled in a shed 8.5 m. long. 5.8 m. wide, and 4.2 m. high? What would be its value at $3.25 a cord? Ans. 207.06 s.; $185.665.

22. A dray is loaded with 60 bags of grain, each bag holding 8 Dl.; allowing 75 K. of grain to the hectoliter, what is the weight of the load in metric tons? Ans. 3.6 T.

23. How many meters of shirting, at $.18 per meter, must be given in exchange for 250 Hl. of oats, at $1.20 per hectoliter?

24. A merchant shipped to France 50 barrels of sugar, each containing 250 lb., paying $2 per cwt. for transportation. He sold the sugar at $.34 per kilogram, and invested the proceeds in broadcloth, at $4 per meter. How many yards did he purchase?

25. A cu. decimeter of copper weighs 8.8 Kg. of a bar of the same metal 15 dm. long, 9.6 cm. thick, at $1.30 a kilogram?

What is the value broad, and 6.4 cm.

Ans. $105.43.

26. How many bricks, each 20 cm. long and 10 cm. wide, will pave a walk 95.4 m. long and 2.1 m. wide; and what will they cost, at $1.75 per hundred? Ans. 10017 bricks; $175.297.

27. What is the value of a pile of wood 40 ft. 6 in. long, 4 ft. broad, and 6 ft. 6 in. high, at $6.50 per dekastere ?

28. What will be the cost of building a wall 96 Dm. 6 m. 8 dm. long, 1 m. 6 dm. thick, and 2 m. 4 cm. high, at $6.75 a cu. meter?

29. A wine merchant imported to Boston 1000 dekaliters of wine, at a cost of $.75 a liter, delivered. At what price per gallon must he sell the same to clear $2000 on the shipment? Ans. $3.596.

30. How many gallons of water will a cistern contain that is 3 m. deep, 2 m. long, and 1.5 m. wide; and what will be its weight in metric tons? Ans. 2377.575 gals. ; 9 T.

TABLE OF EQUIVALENTS.

955. The equivalents here given agree with those that have been established by Act of Congress for use in legal proceedings and in the interpretation of contracts.