(c) Compare the decimal places in the divisor with the number of places that the decimal point in the quotient is placed to the right of the decimal point in the dividend. PRINCIPLEI : The decimal point in the quotient is placed as many places to the right of the decimal point in the dividend as there are decimal places in the divisor. 6. Divide .032375 by .875. 0.037 .875).032375 2625 There are three decimal places in the divisor. Count over three places to the right and place the decimal point in the quotient above the space at the right of the 2 in the dividend. After the decimal point has been located, the division is then performed as if the divisor and dividend were whole numbers. 6125 7. Divide 45 by .15. There are 2 decimal places in the divisor. We must 300. add two zeros after the decimal point and place the decimal point in the quotient above the space at the .15)45.00 right of the second zero in the dividend. Then divide as if the numbers were whole numbers. 8. Divide 11 by 15. .733+ Since 11 is not exactly divisible by 15, we must 15)11.000 add zeros for decimal places and carry out the division 105 as a decimal. The decimal point in the quotient is placed directly above the decimal point in the dividend 50 because there are no decimal places in the divisor. The 45 sign + is used after the second 3 to indicate that there 50 is still a remainder after carrying the quotient out to 45 thousandths. 1The divisor multiplied by the quotient equals the dividend. By the principle for multiplication, the number of decimal places in the dividend equals the sum of the decimal places in both quotient and divisor. Then the number of decimal places in the quotient equals the decimal places in the dividend less the number of decimal places in the divisor. We are really performing such a subtraction when we count off places as directed in the above principle. Divide, carrying out the quotients to 3 decimal places if necessary: 9. 19:1.9 20. 3:8 31. .924:2.64 10. 1:.01 21. 5:8 32. 101:.001 11. 703.7 22. 7-8 33. .0875 : 2.5 12. 45:1.5 23. 15:24 34. 3.67692=2.6 13. 303.75 24. 16:64 35. 10.392;.866 14. 1.2:.06 25. 100:33 36. 21.9912:3.1416 16. 1.75:.25 26. 125 :.05 37. $13.75:-275 16. 45.5:1.3 27. 9.5: 250 38. $43.50: 725 17. .704:22 28. 462.4:7.4 39. $110: 2000 18. .072:.8 29. 30.25:5.5 40. 689.85:16425 10:3 30. 272.25:16.5 41. $97.50: 1500 19. In order to check the position of the decimal point in your result, it is a good plan to estimate each result approximately. For example: 1.3 is contained in 45.5 something over 30 times. 42. A grocer paid $11.40 for a case of 30 dozen eggs. How much did the eggs cost per dozen? 43. An automobile was driven 172 miles in 8 hours during a tour on the Lincoln Highway. Find the average speed in miles per hour. . 44. A gallon of water weighs 8.355 pounds. How much does a quart of water weigh? 46. The expenses of a camping trip for a party of 14 Camp Fire girls were $37.94. If they shared the expenses equally, how much was each one's share? 46. A farmer sold 5.5 pounds of butter to a grocer at $.55 a pound, receiving in exchange sugar at $.11 a pound. How many pounds of sugar did he receive? Exercise 10 1. Divide 42.5 by 10; 375 by 10; .625 by 10. 2. In what direction has the decimal point been moved in each of these examples? How many places has it been moved in each example? In whole numbers the decimal point is not usually indicated, but is understood to be at the right of the number (as 375.). From these examples we find that: Dividing a number by 10 moves the decimal point one place to the left. 3. Divide 87.5 by 100; 35 by 100; 825.42 by 100. 4. In what direction has the decimal point been moved in each of the examples in problem 3? How many places has it been moved in each example? 5. Tell in your own words how to divide a number by 100. 6. How will the decimal point be moved in dividing a number by 1000? By 10,000? Divide without using a pencil: 7. 62.5:10 18. 1414.2: 1000 29. 1465: 100 8. 314.16 : 100 19. $175.25: 100 30. 87.5: 1000 9. 345.8:1000 20. 165:10 31. 55:10 10. 8.66:10 21. $9500 - 1000 32. 866 : 1000 11. 21.5:10 22. 33. 375:10 12. 39.37 : 100 23. 13.75: 100 34. 3.8: 100 13. .75: 1000 24. 87.4:10 35. $2150: 100 14. 22.04:10 25. 153-100 36. 523.6: 1000 15. 272.25: 100 26. 83.5:10 37. $2.80:10 16. 17.32:10 27. 2835 : 1000 38. $35.5: 100 17. 85: 100 28. 62.5: 100 39. $625-1000 How many Exercise 11. Heights of Mountains feet are there in a mile? You will find this number in the first table on the inside of the back cover of this book. How far from the school house would you have to go to walk a mile? If you estimate a mile in this way, it will help you to picture Photo, Underwood and Underwood N. Y. the heights of the mountains given in the following table. Mt. Blanc, shown in the picture,' is slightly less than 3 miles high. Find the height of the following mountains” in miles, carrying the result to at least three decimal places: Height Mountain Continent Height in Feet in Miles 1. Mt. Everest. .29,002 ? 2. Aconcagua South America. .22,080 ? 3. Chimborazo.. South America.. .20,498 ? 4. Mt. McKinley North America. 20,464 ? 6. Kilimanjaro.. . Africa.... 19,780 ? 6. Mt. Logan.. .North America. 19,539 ? 7. Orizaba.. North America.. 18,314 ? 8. Mt. Blanc. Europe... 15,781 2.9509+ 9. Pike's Peak. North America. .14,111 ? 10. Fujiyama.. 12,365 ? 11. Mt. Etna. Europe. .10,835 ? 12. Kusciusko. . Australia 7,836 ? 13. Mt. Whitney .. North America. ... .14,501 ? 14. Mt. Shasta. North America.. 14,380 ? 15. Pike's Peak.. North America... 14,108 ? 16. Mt. Hood.. North America. ....11,225 ? 1This photograph shows the first passage of the Alps by aeroplane. This marvelous feat was accomplished by the French aviator Parmilin. .Asia... . Asia. Exercise 12 1. The record for height ascended in an aeroplane is held by Capt. Schroeder of the U. S. who ascended 36,400 feet in a trial flight in 1920. How many miles high did he go? Express the fractional part as a decimal, carrying the result to 3 decimal places. 2. How much higher is Schroeder's record height than the summit of Mt. Everest? Express this difference as a decimal fraction of a mile. 3. H. G. Hawker ascended to a height of 24,408 feet in 1916. Express this distance in miles, carrying the result to 3 decimal places. 4. The record for height in a gas balloon is 28,750 feet, made by Professor Berson in 1894. How much lower is this than the record for an aeroplane? 5. The record for a dirigible balloon is 9,514 feet. It was made by the Clement-Bayard III, May 20, 1912. The dirigible carried six passengers. Express this record in miles, carrying the result out to 3 decimal places. 6. An aeroplane in a trial flight made an average speed of 1.6 miles per minute. How many miles did it cover if it was in the air 20.5 minutes? 7. Victor Carlstrom, in an aeroplane, ascended 16,500 feet, carrying a passenger, April 30, 1916. How many miles high did the two ascend? What decimal fraction of a mile higher is this than the summit of Mt. Blanc? 8. The first non-stop across the Atlantic was made by Alcock and Brown in 1919. They made a distance of 1980 miles in 16.2 hours. Find the average speed per hour. |