287. To reduce customary weights and measures to those of the metric system.

201. Reduce 280 inches to meters.

Multiply the value of the corresponding unit in the table by the given number of units.

202. Reduce 27 tons to kilos.

203. Find the weight in kilos of 15 gallons of water.

204. Find the capacity in hektoliters of a bin 7 ft. 3 in. long, 3 ft. 10 in. wide, and 2 ft. 2 in. deep.

205. How many square meters in 16 acres?

206. How many liters in 5 bushels ?

207. A grocer buys sugar at 8 cents a pound, and sells it for 22 cents a kilo; how much does he gain or lose on 100 pounds? 208. A man buys 65 liters of wine at $1 a liter, and sells it at $1 a quart; how much does he gain or lose?

209. A man buys 10 tons of coal for $6 a ton of 2240 pounds; what must he get a metric ton to gain $5 on the cost?

210. The latitude of New Orleans is 30°, and that of Chicago is 42°; how many kilometers north of New Orleans is Chicago?

229. What is a simple number? 230. What is a compound number? 232. Give the table of Linear Measure. 234. Give the table of Square Measure. How are the units of this table obtained? 235. What is a rectangle? 236. What are the angles of a rectangle called? 237. What is a square? 238. How is the area of a rectangle found? Explain. 239. If the area and one dimension of a rectangle is given, how is the other found? 241. Give the table of Solid Measure. How are the units of this table obtained? 242. Give the table of Wood Measure. 243. What is a rectangular prism? 244. What is a cube? 245. How is the volume of a rectangular prism found? Explain.

246. If the volume and two of the dimensions of a rectangular prism are given, how is the other dimension found? 248. Give the table of Liquid Measure. 249. Give the table of Dry Measure. How many cubic inches in 4 quarts in Liquid Measure? in Dry Measure? 251. Give the table of Avoirdupois Weight. What is a long ton? 253. Give the table of Time Measure. Give the names of the months and the number of days in each. What is the length of a solar year? 254. What years are leap years? 256. Give the table of Circular Measure. What is the length of a degree on the surface of the earth at the equator? 257. What is a circle? 258. What is an arc? A quadrant? 259. What is a radius? 260. What is a diameter? 261. Into what is the circumference of a circle divided? 263. Repeat the Miscellaneous Table. 265. What is the difference between reduction in these tables and reduction in the decimal system of weights and measures? 267. Give the Rule for reducing higher denominations of a compound number to a lower. 268. What is this kind of reduction called? 269. Give the Rule for reducing a lower denomination to higher denominations. 270. What is this kind of reduction called? 271. How is an example in Reduction Ascending proved? In Reduction Descending? Do these rules of reduction apply when the given number is a fraction? Explain Ex. 94; Ex. 95; Ex. 96; Ex. 97; Ex. 98. 272. What is the difference between operations with compound numbers and operations with simple numbers? Explain Ex. 112. What ought to be done when a fraction occurs in any result? 273. Explain Ex. 117. 274. Give the Rule for finding the difference of time between two dates. Explain Ex. 129. 275. Explain Ex. 131. 276. Explain Ex. 136. 277. Explain how the table of Longitude and Time is formed. 278. Give the table. Explain Ex. 141. 279. Give the Rule for finding the difference of time between two places when their longitude is known. What if the number of degrees is more than 15? In which of two places, at a given moment, is it later in the day? 281. Give the Rule for finding the difference of longitude between two places, when the difference of time is known. 284. In customary weights and measures what is the value of a meter? of a hektar? of a liter of a kilo? What is the metric value of a yard? of a quart? of an English ton? 285. Give all the approximate metric equivalents in this article. 286. How are metric quantities reduced to those in customary use? 287. How are customary weights and measures reduced to those of the metric system?

3. What is 1

of $500? of $ 800? of $1200?

4. How many hundredths of $100 is $1! $6? $21?

5. How many hundredths of anything is of it? of it? of it?of it?

290. Percentage is the term applied to numerical operations in which the unit of computation is one hundred. It is so called from Per Cent, which means by the hundred. Ten per cent of a bushel of corn means ten hundredths of it, or ten parts out of every hundred parts; six per cent of a sum of money is six hundredths of the sum, or $6 out of every $100. Instead of the words per cent it is customary to use the sign, %; thus, 6 per cent is written 6%.

291. The Rate per cent, or the Rate, is the number of hundredths. Thus, 6 % is 10, or 0.06, that is, 6 parts of each hundred parts.

292. The Percentage is such part of the base as is represented by the rate. Thus, the percentage on $200 at 6 per cent is $12.

293. The Base is the number on which the percentage is computed. Thus, $200 is the base on which the percentage is computed in Art. 292; a bushel of corn is the first base mentioned in Art. 290.

294. The Rate, being a certain number of hundredths, may be expressed either decimally, or by a common fraction,

NOTE. When the per cent is expressed by a decimal of more than two places, the figures after the second decimal place are parts of 1 per cent. Thus, 0.125 is 12 or 12 per cent.

295.

Exercises.

6. Write the decimal for 4 per cent.

Ans. 0.04.

7. Write the decimal for 8 %; 12%; 16%; 25 %; 72 %. 8. Write the common fraction for 163 %; 20%; 33 %; 75%; 66% %. 1st Ans. .

9. Write the decimal for %; for %; for % %; for %; for %? 1st Ans. 0.002.

The Base and the Rate given to find the Percentage.

5% of $1, that is, 15 of $1, is 5 cents; and therefore 5% of $4 is

4 times 5 cents, or 20 cents, Ans.

11. What is 5% of $5 of $8? of $12?

12. What is 6% of $8? of $10 of $ 30?

13. What is 10% of $100? 20 % 50 % ?

14. A farmer having 48 sheep lost 25 % of them; how many did he lose?

Solution. 25% = 0.25 = 4; † of 48 = 12, Ans.

15. What is 6% of $250? 7 % ? 8 % ?

16. What is 8% of 600?

17. What is 163 % of 120?

18. What is 12% of $500?

19. What is 83% of 600 bush. of wheat?

20. What is 163 % of 1200 lb. of cheese?

21. A farmer cultivates 25 acres of corn this year, and intends to cultivate 20% more next year; how many acres does he intend to cultivate next year?

22. In an orchard of 900 trees, 33% are peach-trees; how many peach-trees are there in the orchard?

23. A teacher pronounced 56 words for his pupils to spell, but 14% were misspelled; how many words were misspelled?

24. Only 66% of a class of 27 pupils solved a problem given them for a lesson; how many of the class failed?

25. One acre of corn yields 80 bushels, and another acre 20 % more; how many bushels does the second acre yield?