4. Find the weight of this book in pounds. Express this weight in kilograms. Check your work by weighing the book with metric weights, if possible. 5. Express in kilometers the height of a balloon which was observed to be 1500 yd. above the earth. 6. Since an acre contains 160 sq. rd., what approximate part of an acre are 10 ares? An are is equivalent to 4 sq. rd., and a hectare to 2.5 A. 7. How many hectares are there in 50 A.? in 640 A.? 8. The distance by rail from Paris to Berlin is 1084 Km., from Paris to Rome is 1459 Km., and from Paris to Constantinople is 3055 Km. Express these distances in miles. 9. Measure the length and width of your school grounds in feet. Find its area in ares. Check your work by making the measurements in meters and computing the area. 10. A gallon contains 231 cu. in. Express a gallon as cubic centimeters. 11. If a gasoline tank has a capacity of 15 gal., how many liters does it hold? 12. A rate of 40 mi. per hour is how many meters per second? 13. An importer buys 1200 m. of silk for $3000. What should be the selling price per yard if the merchant plans for a gross profit of 0.45 of the cost price? 14. If a hektoliter is approximately equivalent to 2.2 bu., how many bushels of wheat are needed to fill an order for 5000 H1. of wheat? 15. At 50¢ per kilogram, how many pounds can be bought for $1? for $4.75 ? for $9.50 ? 16. A dirigible balloon with a capacity of 1000 cu. m. is filled with helium gas from small tanks, each containing 60 cu. ft. How many tanks are required to fill the balloon? 17. Express a cubic inch in cubic centimeters. What is the weight in grams of 1 cu. in. of distilled water? CHAPTER IV COMPARING QUANTITIES PERCENTAGE Per cent. The expression per cent means hundredths; that is, a number given as a per cent indicates a number of hundredths. It is evident that there are three ways of expressing a number of hundredths: (a) by a common fraction, as 72; (b) by a decimal fraction, as 0.72; and (c) by the per-cent symbol, as 72%. The three forms all have the same meaning, but the last form, that of a per cent, is the common business form. ORAL EXERCISES 1. Express each of the following as an equivalent fraction with the denominator 100: ;;; 20 ; ; ; ; ; 17. 1; 1; 3 6 3 2. Using the results of Ex. 1, express each fraction as a decimal; as a per cent. 3. Express each of the following as a per cent: 0.32; 0.45; 0.5; 0.33; 0.12; 0.62; 1.00; 2.50. 4. Express each of the following as a decimal: 15%; 56%; 6%; 121%; 61%; 81%; 200%; 250%. 5. Express each of the following as a common fraction in lowest terms: 0.50; 0.73; 66%; 1.25; 3%; 80%; 121%; 871%; 331%; 125%; 1331%; 1%. Percentage. The process of computing by per cents is called percentage; a term also applied outside of business to the result of finding a per cent of a number. Per cent of a number. The process of finding a per cent of a number is that of finding a given number of hundredths of the number; namely, multiplying the number by a fraction or a decimal which represents the given number of hundredths. Thus 25% of $100 means $100 × 4, and 17% of $125 means $125 × 0.17. Fractional values of certain per cents. Certain per cents are readily expressed as equivalent common fractions, and in such cases the process of finding a per cent becomes that of finding a fractional part. The following list of fractional equivalents of certain per cents should be memorized, since these per cents are used in many business computations: Solution. Since 121% is of the number, then 12% of 120 is 120 × 1, or 15. 9. 60% of $220; of $300. 10. 66% of $300; of $105. 11. 831% of $1080; of $60. 12. 81% of $960; of $720. 13. 80% of $150; of $175; of $210. 14. 75% of $160; of $80; of $12.60; of $8.28. 16. 871% of $824; of $728; of $648. Finding a per cent of a number. When a per cent of a number such as 3%, 4%, 5%, 7%, and so on is to be found, the following method of multiplying mentally should be used. EXAMPLE. Find 7% of $200. Solution. Here 7% of $200 means $200 × 0.07. It is seen at once that 1% of $200, or $200 × 0.01, can be found by simply moving the decimal point two places to the left, giving $2. Then 7% of $200 is $27, or $14. ORAL EXERCISES Find the following: 1.2% of $100. 2. 2% of $400. 3. 2% of $150. 4. 2% of $50. 5.3% of $100. 6. 3% of $500. 7.3% of $120. 8. 3% of $80. 9. 3% of $20. 10. 4% of $100. 11. 4% of $450. 17. 6% of $200. 21.8% of $125. 22.8% of $75. 23. 10% of $240. 24. 10% of $575. 25. 12% of $400. 26. 15% of $200. 27. 21% of $100. 28. 21% of $500. 29. 31% of $400. 30.41% of $200. General method of finding a per cent of a number. When neither of the above methods can be readily applied, the student should see that finding a per cent of a number is only the familiar operation, expressed in different language, of multiplying by a decimal. Emphasis should be placed upon the relation of percentage to the decimal processes with which the student is familiar. In this way many of the difficulties of the student may be removed. EXAMPLE. Find 15% of $725. Solution. By the definition of a per cent, 15% of $725 means $725 × 0.15. The work is set down as shown at the right. Then multiplying as with decimals, the result is found to be $108.75. EXERCISES $725 0.15 3625 725 $108.75 1. Find 7% of $225; of $310; of $165.25; of $535.75. Unless otherwise directed, the student should find such per cents only to the nearest cent. 2. Find 12% of $115; of $75.25; of $96.15; of $210.15. 3. Find 28% of $540; of 930 bu.; of $458; of 36 gal. 4. Find 17% of $375; of $1240; of 25 T.; of 4250 lb. 5. Find 106% of $650; of $775; of $1240; of $2465. The student should see that 106% may be written as 1.06. 6. Find 112% of $880; of $1200; of $535.75; of $476.95. 7. Find 27% of $450; 2.7% of $450; 0.27% of $450; 0.027% of $450. 8. Find the difference between 1.4% of $760 and 0.14% of it. 9. Find 66% of $720; of $2400; of $180; of $324. Remember to use a short method. 10. Find 831% of 1200 pupils; of 1620 lb.; of 4500 lb. 11. Find 125% of $4.88; of $525; of $42.75; of $563.30. Since 125% 14, then 125% of $4.88 is 5 x of $4.88, or 5 × $1.22, which is $6.10. 12. Find 66% of 640 A.; of $1260; of 5610 sq. ft. 13. Find the difference between 162% and 331% of $420. |