REDUCTION. 586. A denominate number in the metric system can be reduced to higher or lower denominations by the removal of the decimal point. 1. In measures of volume, since it requires 1000 of each denomination to make one of the next higher, the decimal point must be removed three places. 2. In measures of surfaces, since it requires 100 of each denomination to make one of the next higher, the decimal point must be removed two places. 3. In other measures remove the decimal point one place. EXERCISES. 587. 1. Reduce 15675cm to kilometers. 2. Reduce 7560sq m to ares. 3. Write 6734cl as liters; as hektoliters. 4. Write 43628mg as grams; as kilograms. m 5. Write .75cu as liters; as hektoliters. 6. Write 876.37sq cm as square meters; as ares. A cubic centimeter of water weighs 1 gram. 8. What is the weight in dekagrams of .045cum of water? 9. What is the weight in kilograms of 13 of water? 10. How much will a cubic meter of water weigh in kilograms? Express the same quantity of water in liters. 11. What is the amount of 65750.75' of water in cubic meters? What is its weight in kilograms? A milliliter of water weighs 1 gram. 12. What will 60' of mercury weigh, mercury being 13.5 times as heavy as water? The weight of any substance compared with the weight of an equal bulk of water is called its specific gravity. The sp. gr. of mercury is 13.5. 13. Find the weight in grams of a cubic decimeter of iron (sp. gr. 7.21). 14. What is the weight in kilograms of a cubic meter of ice (sp. gr. 0.92)? 15. Which is the cheaper and how much, to buy cloth at $3 per meter, or at $2.90 per yard? 16. How many ares are there in a rectangular field 62m long and 43.6m wide? 17. How much carpet a meter in width, is required to carpet a room 5.3 meters long and 4.2 meters wide? 18. How many liters of water are there in a tank 2.6m long, 2m wide, and 6dm deep? 19. How long must a pile of wood be, to contain 12 steres, if it is 3.5 meters high and 3.8 meters wide? 20. A barrel of flour contains 196 pounds. How many kilograms or kilos does it weigh? 21. A bin is 3 meters square and 2.5 meters high. How many hektoliters of wheat will it hold? 22. What weight of mercury will a vessel contain whose capacity is 25cu cm ? 23. A tank is 4m long, 36dm wide, 76cm deep. How many liters of water will it hold? 24. A vat is 6.4m long, 3m wide, and 2.8m deep. How long will it take a water-pipe to fill the vat, if 2.9D1 flow into it per minute? 25. A platform bears a weight of 60 pounds per square foot. What is the weight in kilograms per square meter? 26. A man bought 360 bu. of wheat at $.95 a bushel, and sold it at $2.95 a hektoliter. How much did he gain? 27. The dimensions of a box are 3.5m, 1.8m, and 0.8m. What are the contents in cubic yards? 28. A room is 5.2 meters long, 4.5 meters wide, and 3.2 meters high. What will be the cost of plastering it at 35 cents per square meter? 29. How much will a merchant receive for 3.68 of wine, if he sells it at $2.50 per gallon? 30. What is the weight in kilograms of 2583 cu cm of water? 31. How much will 4 tons of coal cost at $.75 per quintal ? 32. Reduce 20 lb. 8 oz. Avoirdupois to hektograms. 33. How many revolutions will be made by a wheel 9 ft. in circumference in passing over a distance of one kilometer? 34. Which is the larger and how much, a cask which holds 21D or one which holds 43 gallons? 35. Change 10 hektograms to pounds Avoirdupois weight; Troy weight. 36. Find the weight in grams of a gallon of water. 37. What price per pound is equivalent to $2.20 per kilogram? 38. A square foot is what part of a square meter? 39. How many centares are there in a garden plot 10 feet square? 40. The specific gravity of granite is 2.9. What is the weight of a block 50cm long, 25cm wide, 12cm thick, in kilograms? in pounds? 41. What is the weight in kilograms of a cubic foot of water? 42. How many meters are there in 2 mi. 40 rd. 12 ft. ? 43. How many gallons are there in 24 dekaliters ? 44. A man bought 50Kg of sugar for $5.51. How much did he pay per pound? 45. How many gallons will a cistern contain which is 3m square and 2m deep? 46. What price per bushel is equivalent to $6.60 per hektoliter? 47. If the specific gravity of copper is 8.8, what is the weight in hektograms of a cubic decimeter of the metal? 48. If a bushel of oats weighs 32 pounds, what is the weight in kilograms of 40 bu.? 49. If a body weighs 7.35K in air and 4.41Kg in water, what is its specific gravity? 50. What is the weight in dekagrams of 44 cubic decimeters of zinc, if the specific gravity is 6.86? 51. A cask of olive oil containing 2 cost $36.32. What was paid per quart for the oil? 52. If a silver dollar weighs 412 grains, how many grams does it weigh? 53. If a quire of paper is .588cm thick, what is the thickness in millimeters of a single sheet? 54. What is the value of 20 qt. of sulphuric acid at 2 cents a pound, if the specific gravity is 1.841? 55. A rectangular vessel is 5m long, 9dm wide and 3m deep. Find its capacity in cubic meters. What is the weight of distilled water at its greatest density that it will hold. 56. A liter is .264 of a gallon. How many grams will a gill of water make? 57. A rectangular cistern is known to hold 25. If its length is 2m, its breadth 1.5m, what is its depth? 58. An importer bought silk at $1.15 per meter and sold it at a profit of 20% per yard. How much did he get for it per yard? 59. Mercury is 134 times as heavy as water, or its specific gravity is 13.5. How many pounds will a vessel hold whose capacity is 35eu cm ? 60. A man paid 800 francs for 100 liters of wine. What price did he pay for it per gallon? 61. A cubical block of silver whose dimensions are 2dm was sold at 20 per dekagram. If the specific gravity of silver is 10.5, for how much did it sell? 62. If alcohol is .8 as heavy as water, how many pounds Avoirdupois will 1250eu em of alcohol weigh? MEASURES OF EXTENSION. 588. Measures of Extension are used in measuring lengths, distances, surfaces, and solids. 3 Barleycorns 4 Inches 6 Feet 3 Feet 5 Paces 8 Furlongs 1.15 Statute Miles 3 Geographical Miles 60 Geographic Miles } 69.16 Statute Miles = 1 Inch. Used by shoemakers. = 1 Hand. Used to measure the height of horses. =1 Fathom. = 1 Pace. = 1 Rod. = 1 Mile. Used to measure depths at sea. }Used in pacing distances. = 1 Geographical, or Nautical Mile. = 1 League. = 1 Degree { of Longitude on the Equator. 1. The length of a degree of latitude varies. 69.16 miles is the average length, and is that adopted by the United States Coast Survey. 2. The standard unit of length is identical with the imperial yard of Great Britain. 3. The standard yard, under William IV., was declared to be fixed by dividing a pendulum which vibrates seconds in a vacuum, at the level of the sea, at 62° Fahrenheit, in the latitude of London, into 391,393 equal parts, and taking 360,000 of these parts for the yard. The following denominations also occur: The span 9 inches; = 1 common cubit (the distance from the elbow to the end of the middle finger) 18 inches; 1 sacred cubit = 21.888 inches. = 418 |