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133. In a board 4m long and 0.4m wide, how many square decimeters?

134. If a stone 1.25 m long, 0.72m wide, and 0.4m thick, weighs 1 ton, what is its specific gravity?

228. QUESTIONS.

180. Why is the decimal system of weights and measures called the metric system? Where is it used? 181. Repeat the table of Linear Measure? 182. What is the length of the meter? How are the smaller denominations generally written and read? 184. How are the names of the divisions of the unit formed? The names of the multiples? 185. Deci, centi, milli correspond to what in United States Money? 186. What may be taken as the unit in Linear Measure? 189. How is reduction performed? 192. How are the units in the table of Square Measure formed? Repeat the table. 193. What is the unit for land measure? How many square meters in a hektar? 194. How many places for each denomination in Square Measure? Why? 197. What is a rectangle? 198. What are the angles of a rectangle called? 199. What is a square? 200. How is the area of a rectangle found? Explain. 201. If the area and one dimension of a rectangle are given, how is the other found? 203. How are the units in the table of Cubic Measure formed? Repeat the table. 204. What is the unit for wood measure? 205. How many places for each denomination in Cubic Measure? Why? 208. What is a rectangular prism? 209. What is a cube? 210. How is the volume of a rectangular prism found? Explain. 211. If the volume and two of the dimensions of a rectangular prism are given, how is the other dimension found? 213. Repeat the table of Capacity Measure. What is a liter in cubic dimensions? A milliliter? A kiloliter? 214. How are these measures written? 217. Repeat the table of Weights. 218. How are these measures written? 219. What is a gram? A kilogram? A ton? Give the weight of the silver coins of the United States. Of the nickel fivecent piece. 222. What is meant by specific gravity? Explain. 223. What is the specific gravity of gold? Of mercury? Of maple? 224. If the specific gravity and magnitude of a body in metric measures are given, how is its weight found? 226. Explain the formation of the names in the decimal system of money, weights, and measures.

COMPOUND NUMBERS.

229. A Simple Number consists of but one kind or denomination; as 2, $4, 8 books, 5 men, 6 days, 10 miles.

230. A Compound Number is composed of two or more denominations of the same kind; as 4 days and 7 hours; 3 dollars, 2 cents, and 5 mills; 5 rods, 4 feet, and 6 inches.

NOTE 1. Although the quantities in the tables of the decimal system of money, weights, and measures are of different denominations, yet, as their relations are in the decimal scale, they can be written and treated as simple numbers, any denomination of the table being taken as the unit.

NOTE 2. The several parts of a compound number, though of different denominations, are yet of the same general nature; thus, 2 weeks, 3 days, and 6 hours are of like nature, and constitute a compound number; but 2 weeks, 3 miles, and 6 quarts are unlike in their nature, and do not constitute a compound number.

231. The following tables of weights and measures are now generally used in the United States.

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4. What is the cost of making a mile of road at $ 1.50 a rod?

5. How many feet is it round a room that is 16 by 12 feet?

6. How many feet in 6 rods?

7. How many yards in 48 feet?

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NOTE. The units of square measure, so far as they are the same in name, are obtained by squaring (that is, taking twice as a factor) the units of the table of linear measure.

235. A Rectangle is a plane (or flat) surface bounded by four straight lines and having all its angles equal.

236. The figure is called rectangular, and the angles right angles.

237. A Square is a rectangle whose sides are equal.

238. To find the area of a rectangle.

A

C

D

Let ABCD be a rectangle whose B base AD is 5 inches in length, and whose altitude A B is 3 inches. If AD is divided into 5 equal parts and A B into 3, and lines are drawn through the points of division, the rectangle will be divided into squares, each containing 1 square inch; and the rectangle will evidently contain 5 × 3, or 15, of these squares; that is, its area = 5 × 3 square inches = 15 square inches. Therefore,

The area of a rectangle is the product of its length and breadth.

239. The area of a rectangle divided by the length will give the breadth, and the area divided by the breadth will give the length.

240. Oral Exercises.

12. How many square inches in a rectangle 9 in. long and 7 in. wide? (See Art. 238.)

13. How many square feet in 9 square yards?

14. How many square rods in 4 acres?

15. How many acres in 400 square rods?

16. How many square yards in 72 square feet?

17. What part of an acre is 40 square rods? 80 square rods? 120 square rods?

18. How many square rods in of an acre?

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NOTE. The units of this table are obtained by cubing (that is, taking three times as a factor) the units of the table of linear measure.

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245. To find the volume of a rectangular prism.

Let ABCD, EFGH be the rectangular prism whose base is a rectangle 5 inches from A to D, and 3 from A to B, and whose altitude A E is 4 inches.

E

N

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F

H

D

G

the point K, one inch from A, it will evidently cut off 15 cubic inches, that is, 5 × 3 × 1 cubic inches. If, in like manner, a plane passes through M, it will cut off 15 more; and so on. That is, the rectangular prism contains 5 × 3 × 4 cubic inches 60 cubic inches. Therefore,

The volume of a rectangular prism is equal to the product of its three dimensions.

246. The volume of a rectangular prism divided by the area of its base will give the altitude; the volume divided by the area of one end will give the length; and the volume divided by the area of one side will give the breadth or width.

247. Oral Exercises.

19. How many cubic feet in a cubical block whose edge is 2 feet? 20. How many cord feet in 48 cubic feet of wood?

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