Notes.-1. Notice that the abbreviations for measures larger than the unit begin with capital letters, the abbreviations for measures smaller than the unit begin with small letters. Let the pupils construct, for class use, oral exercises similar to the following, on all the tables, using the appropriate abbreviations. 2. The names of the denominations may be readily learned by repeating only parts of the names, thus: milli, centi, deci, meter, deka, hekto, kilo, myriameter. As these are repeated, the learner should think of the meanings of the prefixes, which are as follows: The Meanings of the Prefixes. 1. How many meters (m.) in a myriameter (Mm.)? In a kilometer (Km.)? In a hektometer (Hm.)? In a dekameter (Dm.)? (Myria ten thousand; kilo a thousand; hekto a hundred; dekaten.) 2. How many dekameters (Dm.) in a hektometer (Hm.)? In a kilometer (Km.)? In a myriameter (Mm.)? 3. How many hektometers (Hm.) in a myriameter (Mm.)? In a kilometer (Km.) ? 4. How many Km. in a Mm.? 5. What part of a m. is a decimeter (dm.)? A centimeter (cm.)? A millimeter (mm.)? (Deci one tenth; centi = one hundredth; milli = one thousandth. Compare decimal, cent, mill.) 6. How many mm. make one cm.? 7. How many cm. make one dm.? 8. What part of one Km. is one cm.? One dm.? One m.? One Hm.? One mm.? 9. What part of two cm. are two mm.? Of five dm. are five cm.? Of seven Hm. are seven m.? 10. How many ml. in 1.5 cl. ? .75 dl. ? 11. How many grams in .25 Mg. ? % Dg.? SLATE EXERCISES. 1. Write the Linear Measure table, thus: Table. 10 millimeters = 1 centimeter. 10 centimeters = 1 decimeter, etc. 2. Write the Dry and Liquid Measure table in the same way. (The table of Liters.) 3. Also the table of Weights. (The table of Grams.) 4. Write in full the denominations indicated by m., cl., Dg., dm., Kl., cm., Mm., Hl., mm., Mg., Dm., cg., ml., Kg., Hm., Dl., mg., Km., Hg., dl., g., dg., 1. 5. Read 858.65 m., giving separately the denomination of each figure. Ans., 8 hektometers, 5 dekameters, 8 meters, 6 decimeters, 5 centimeters. 7. Write 3 Kg. 5 g. 3 cg. 4 mg. in the denomination of the prime unit (grams). Ans., 3005.034 g. Note. Be careful to fill all intervening vacant orders with ciphers, so that each digit shall by its position indicate its denomination. In the number given above, there are no hektograms, no dekagrams, no decigrams, hence the ciphers. 8. In the same way write : 5 Hl. 7 Dl. 8 dl. 2 cl. 5 ml. 1 Mm. 6 Hm. 5 m. 3 mm. 4 Hm. 5 Dm. 3 dm. 8 mm. 7 Dg. 3 g. 9 cg. 1 mg. 9 Kl. 8 Dl. 2 1. 3 dl. 5 Mm. 9 Km. 5 Hm. 8 Dm. Reductions. 1. Reduce 25.325 kilometers to decimeters. 1 Km. = 10 Hm., hence 25.325 Km. = 253.25 Hm. 1 m. = 10 dm., 66 253.25 Hm. = 2532.5 Dm. 66 66 2532.5 Dm. = 25325. m. Thus, in Reduction Descending, each step removes the decimal point one place to the right. 261. Rule. To reduce a higher metric denomination to a lower: Remove the decimal point one place to the right for each step of the reduction. Annex ciphers, if necessary. 2. Reduce 435.32 dm. to Hm. 10 dm. = 1 m., hence 435.32 dm. = 43.532 m. 10 m. = = 4.3532 Dm. 1 Dm., 43.532 m. = 66 10 Dm.= 1 Hm., 4.3532 Dm. = .43532 Hm. Thus, in Reduction Ascending, each step removes the decimal point one place to the left. 262. Rule. -To reduce a lower metric denomination to a higher: Remove the decimal point one place to the left for each step of the reduction. Prefix ciphers if necessary. The two foregoing rules may be given in one, thus: 263. Rule. To reduce a number from one metric denomination to another: Remove the separatrix from the right of the given denomination to the right of the denomination required, and change the abbreviation accordingly. EXERCISES. 1. How many cm. in 7 m.? How many dg. in 3 Dg.? 2. How many meters in 3.15 Km.? How many liters in 6.17 Hl.? How many grams in 18.416 mg.? 3. Express the sum of 231 cm., 2859 dm., 354 mm. in meters. 4. Add 28.35 m., 200.03 m., 123.9 m., 456.7 m., and express the answer in hectometers. 5. Express in grams and add 127 dg., 7200 Hg., 8.83 Kg. 6. Find how many grams remain if you take 8 Kg. from 58 Kg. 7. Carl is told to measure the water in a vessel containing 14.31 1., with a cup holding 3 cl. How often will he have filled the cup, if his measurement is correct? 8. The circumference of May's hoop measures 3.8 m.; how many times will it turn in rolling a distance of 53.2 m.? 9. A nickel 54 piece weighs 5 g. How many such pieces can be made of a bar of coin metal weighing 5 kilograms. 10. Add 4.97 m., 21 cm., 6.03 m., 9.137 m., 38 dm. 11. Subtract 9 Km. 6 Dm. 7 m. 3 dm. from 1 Mm. 12. Multiply 18.28 Dg. by 29. Express the product in cg. 13. Divide 5238.45 1. by 8. 14. Sold 14.23 1. at $.50 a dl. Express the quotient in Dl. How much did I receive? 15. A train runs 54.5 Km. an hour. How far in 4.5 hours? 16. How many kilometers of telegraph wire are needed to connect two stations, if the distance between two poles is 43 m., and there are 516 poles between the stations? (517 × 43.) 17. How many m. of fence are needed to close in a field 535.5 m. long and 285.5 m. wide ? 18. What will be the profit on 14 Hl. of vinegar, bought at $4 a Hl. and sold at 84 per liter? 19. What will be the profit on 10 g. of calomel bought for 504, if sold in powders of 5 dg. at 54 each? 20. A merchant bought cloth at $1.14 a m.; for how much per m. must he sell it to gain 1/3 of the cost? 21. If I buy 6.328 Ml. at 54 a 1., and sell it at 24 a dl., do I lose or gain? How much? 22. How many 1. of grain will fill a box 7 m. long, wide, and deep? |