Multiples of the Meter. § 12. Besides the meter and its subdivisions, there are longer measures, which are multiples of the meter. § 13. The děk'a-meter is ten times as long as the meter. NOTE. The prefix deka- means tenfold. § 14. The hěk'to-meter is a hundred times as long as the meter. NOTE. The prefix hekto- means a hundredfold. § 15. The kiľ'o-meter is a thousand times as long as the meter. NOTE. The prefix kilo- means a thousandfold. § 16. The myria-meter is ten thousand times as long as the meter. NOTE. The prefix myria- means ten thousandfold. NOTE. Of these longer measures, the kilometer is used in measuring distances on roads, canals, rivers, etc. The other measures are much less frequently used; the myriameter hardly ever. § 17. Exercises on the Multiples of the Meter. a. Measure off a string ten meters long. What name is given to the length of this string? NOTE. The string may be used in measuring distances. For this purpose it will be well to make knots at the end of each meter. b. Measure in dekameters and meters the length and breadth of the school-yard; of a garden; of a field, etc. c. Measure off in the street, or other convenient place, a distance of 10 dekameters. What name is given to this distance? d. Walk from the beginning to the end of the distance thus measured off, and count your paces. How many of your paces make a hektometer? e. How many of your paces would make a kilometer? f. How many kilometers from your home to the school-house? MEASURES OF LENGTH. g. How long does it take you to walk a kilometer? h. How many kilometers can you walk in an hour? 7 i. If 1500 of your paces make a kilometer, how many make a dekameter? § 18. To express distances in meters and multiples of a meter, we write meters in the units' place, dekameters in the tens' place, hektometers in the hundreds' place, and so on. 19. To express a distance in kilometers, we write kilometers in the units' place, and then hektometers, dekameters, and meters will be written in the tenths', hundredths', and thousandths' places respectively. Thus, if the distance from one town to another is found to be 9780 meters, the usual form of writing would be 9.78 kilometers. NOTE. The greatest distances are usually expressed in kilometers. Thus, the distance of the earth from the sun is about 149000000 kilometers. § 20. The abbreviations used in writing are: For the dekameter, Dm; for the hektometer, Hm; and for the kilometer Km. Addition, Subtraction, Multiplication, and Division of Metric Numbers. § 24. ILLUSTRATIVE EXAMPLE. add 14.83 Dm, 75.6 Hm, and 948 cm. WRITTEN WORK. 148.3 m 7560. 9.48 14.83 D Dm 75.6 Bm = = 948 cm = 7717.78 m Change to meters and Explanation. When these expressions have been changed to meters, they are all of the same denomination, and the sum is found in the same way as in the addition of simple numbers. § 25. Numbers expressing metric measures and weights are added, subtracted, multiplied, and divided by the same rules as apply to simple numbers. § 26. Examples for the Slate. 19. Add 5.6, 24.07 m, 30.5m, and 7.508 m. 20. Express as meters and add 582 cm, 6428 dm, and 495 mm 21. Express as meters and add 369 Dm, 4073 Hm, and 5 Km. 22. Add 48.06m, 709.63m, 3708.9", 800.9", and express the answer in kilometers. 23. If 7 Km be taken from 42 Km, how many meters remain? 24. From 87.04 m take 42 cm. 25. The distance round a certain park is 2.58 kilometers. How many meters will a man go who rides around it six times? 26. A school-boy walked one third around the above park in 12 minutes. How many meters did he walk in 1 minute? 27. How many kilometers in 36.68mx 2004 ? 28. Divide 38.07 m by 4 and by 3, and add the answers. 29. Ellen's hoop is 3.6m around. How many times will it turn in rolling a distance of 1.08 km ? MEASURES OF SURFACE. 9 MEASURES OF SURFACE. § 27. The units used in measuring surfaces are squares, each having sides equal to a unit of long measure. Thus, a square meter is a square having sides one meter long; a square decimeter is a square having sides one decimeter long; etc. § 28. Exercises. a. How many square decimeters in a square meter? Illustrate by drawing a square meter on the blackboard or on the floor and dividing it into square decimeters. b. How many square centimeters in a square decimeter ? Illustrate by drawing a square decimeter on your slate and dividing it into square centimeters. c. How many square meters in a square dekameter? § 29. The square dekameter, when used as a unit of land measure, takes a special name, and is called an ar. One hundredth of an ar, which is one square meter, is called a centar. A hundred ars, equal to one square hektometer, is called a hektar. § 30. Square Measure. 100 square millimeters (sq mm) = 1 square centimeter (sq cm). 100 square centimeters = 1 square decimeter (sq dm). = 1 square meter (sq m) = 1 centar (ca). = 1 ar (a). = 1 hektar (Ha). 100 square decimeters § 31. As the units of square measure form a scale of hundreds, in writing numbers expressing surface two decimal places must be allowed for each denomination. Thus, 45 sq m 4 sq dm 86 sq cm are written 45.0486 sqm; and 7 H 6a 5 ca are written 706.05a. На § 32. Examples for the Slate. 30. How many square meters of carpeting will be required to carpet a room 5.3m long and 4.5m wide ? 31. How many meters of carpeting 0.7" wide will be required to carpet a room 4m long and 3.5m wide ? 32. What is the cost of polishing the surface of a rectangular piece of marble 2.8 meters long and 1.2 meters wide, at $2.50 per sq. meter? 33. In a piece of land 15m long and 14.5m wide are how many square meters or centars? how many ars? 34. Express the following in ars and add them: 1.3 hektars, 155.5 ars, 43 hektars, 26 centars. 35. A had 6 hektars, 7 ars, 9 centars of land, and sold 0.2 of it at $54 an ar. How much did he receive for what he sold ? MEASURES OF VOLUME. § 33. The units used in measuring cubic contents, or volume, are cubes, each having its edges equal to a unit of long measure. Thus, the cubic meter is a cube having edges one meter long; a cubic decimeter is a cube having its edges one decimeter long; etc. § 34. Exercises. a. How many cubic decimeters in a cubic meter? b. How many cubic centimeters in a cubic decimeter? Illustrate by means of a cubical block having edges one decimeter long, marked off into centimeters. § 35. The cubic meter, when used as a unit of measure for wood and stone, takes a special name, and is called a ster. § 36. The cubic decimeter, when used as a unit of liquid or dry measure, is called a liter. |