WEIGHTS. 445. The primary unit of weight is the gram. 446. A gram is the weight of one cubic centimeter of pure water at the temperature of 4 degrees centigrade (=39.2 degrees Fahrenheit), at which temperature water has its greatest density. 447. Larger and smaller weights are derived from the gram by taking decimal multiples and subdivisions. NOTE I. The gram, kilogram, and metric ton are the only units used in actual weighing, except by jewellers, druggists, and those who weigh very small or very expensive articles, like gold or powerful medicines. NOTE II. The kilogram is generally called the kilo. The kilo is the unit of weight for weighing common articles, such as sugar, tea, etc. NOTE III. The metric ton is used to weigh very heavy articles, like hay, coal, etc. 449. Examples for the Slate. 47. At $0.60 a kilo for honey, what is the cost of 5.15 kilos? 48. At $11 per T. for coal, what will the coal cost to keep a fire one week if 30 kilos are burnt each day? 49. What weight of mercury will a vessel contain whose capacity is 10cu em, mercury being 13.5 times as heavy as water? 50. If marble is 2.7 times as heavy as water, what is the weight of a pedestal 1 meter square at each end and 2 meters high? EQUIVALENTS. 182 450. Table of Equivalents. The equivalents here given agree with those that have been established by Act of Congress for use in legal proceedings and in the interpretation of contracts. inch. 6.452 sq. centimeters. 1 sq. centimeter = 0.1550 sq. 1 sq. decimeter = 0.1076 sq. foot. 1 sq. foot = 1 sq. yard 0.8361 sq. meter. 1 ar= 3.954 sq. rods. = 1 sq. meter = 1.196 sq. yards. 1 sq. rod = 25.293 sq. meters. 1 acre = 0.4047 hektar. 1 hektar = 2.471 acres. 1 sq. mile = 2.590 sq. kilometers. 1 sq. kilometer = 0.3861 sq. mile. 16.387 cu. centimeters. 1 cu. centimeter = 0.0610 cu. inch. 1 cu. foot = 28.317 cu. decimeters. 1 cu. decimeter = 0.0353 cu. foot. 1 pound Troy = = = 0.908 dry quart. 1 dekaliter = 1 hektoliter 2.8375 bushels. = 0.03527 ounce av. 1 gram 2.2046 pounds av. 1 metric ton = 1.1023 tons. 1 gram = 31.1035 grams. 1 gram = 15.432 grains Troy. 0.03215 ounce Troy. 0.3732 kilogram. 1 kilogram = 2.679 pounds Troy. 451. To change numbers in the metric system to equivalents of the old system: [Use preceding table.] Examples. 51. In 48 meters how many feet? 52. If you travel 50 kilometers in a day, how many miles do you travel? 53. Change 18 hektars of land to acres. 54. How many inches long is an insect that is 5.2 centimeters long? 55. How many pounds av. are there in 85.6 kilos of salt? 56. How many gallons are there in 24 kiloliters? 57. In 20 metric tons how many tons? 452. To change numbers in the old system to equivalents of the metric system: [Use preceding table.] Examples. 58. Change 25 miles to kilometers. 59. In 200 acres are how many hektars? 60. How many liters will a cistern hold that measures on the inside 5 feet in length, 4 feet in width, and 4 feet in height? 61. In 3 rods how many meters? 62. Change 18 qt. 1 pt. to liters. 63. In 1 lb. 7 oz. 18 pwt. of gold, how many grams? 64. What is the weight of a barrel of flour (196 lbs.) in kilograms? 453. Approximate Equivalents. The equivalents here given are accurate enough for most purposes, and are easy to remember. SECTION XIV. PERCENTAGE. 454. Find 18 of 500 men. Ans. 45 men. A number obtained by finding a number of hundredths of another number is a percentage of that number. 455. The number of which the percentage is found is the base of that percentage. In the above example what number is the percentage? the base? 456. If a person having $2000 should gain a sum equal to of it, how much would he then have ? 2000 = 200; 2000 + 200 2200. Ans. $2200. = The sum of the base and percentage is the amount. 457. If a person having $2000 should lose of it, how much would he have left? 2000 × 1 = 200; 2000-200-1800. Ans. $1800. The part of the base left after a percentage is taken away is the remainder. In the above examples what number is the amount? the remainder? 458. The number of hundredths which the percentage is of the base is the rate per cent, generally called the per cent. Thus, 10 of anything is 7 per cent of it. NOTE. Per cent is a contraction of the Latin per centum, and means by the hundred. 459. Oral Exercises. a. Find 1 per cent of 600; 7 b. Find 10 per cent of $250; per cent; 20 per cent. To express a given Per Cent. 460. The sign % is used for the words per cent. Thus, 5 % means 5 per cent. 461. Any per cent may be expressed as a common fraction, as a decimal, or with the sign for per cent, %. Thus, 1 per cent may be expressed 186, 0.01, or 1%. 462. Express the following in the three forms given above. a. 2 per cent. c. 7 per cent. e. 175 per cent. f.per cent. 463. Express the following as common fractions, and change them to their smallest terms: To find the Complement of a given Per Cent. 464. What is the difference between 100 % and 25 % ? The difference between 100 % and any given per cent less than 100 % is the complement of the given per cent. 465. Oral Exercises. a. What is the complement of 75%? 40%? 60%? 33}%? 61%? 15%? b. What is the complement of 62%? 16%? 37%? 18%? 87%? 72%? |