Answer, .000675. 11. Multiply 125.015 by .001. Answer, .125015. Answer, .438496. 23. Multiply .0001 by 100. Answer, .01. 24. Multiply 1 tenth by 1 hundredth. Answer, .001. 25 Multiply 1 hundred by 1 ten-thousandth. Answer, .01. 26. Multiply 43 thousandths by 21 ten-thousandths. .0000903. 27. Multiply 40000 by 1 millionth. Answer, .04. 28. Multiply .09375 by 1.064. Answer, .09975. Answer, 29. A pump delivers 8.54 gallons of water per stroke. The pump is a double-acting pump and makes 48 strokes per minute. How many gallons of water will it deliver in 1 hour? Answer, 24,595.2 gals. 30. The specific gravity of ice is .92 of the weight of an equal bulk of fresh water. A cubic foot of water weighs 1,000 ounces. What is the weight of 8.65 cubic feet of ice? Answer, 7,958 ounces, or 497.375 pounds. 31. An engine makes 68.57 revolutions per minute. How many revolutions will it make in 37.5 minutes? Answer, 2,571.375 revolutions. 32. A cubic foot of salt water weighs 64.375 pounds. What will a column of water 1 foot square and 60.5 feet high weigh? Answer, 3,894.6875 pounds. 33. What will be the pressure per square inch due to a head of salt water 60.5 feet high? Answer, 27.046+ pounds. 34. The steam piston of a pump has an area of 150.94 square inches. What will be the total pressure on the piston if the cylinder is filled with steam at 200 pounds per square inch? Answer, 30,188 pounds. 35. If .15 of the entire energy supplied to above pump is used in running the pump, lifting the water to the point of discharge, overcoming the friction of the valves, and the weight of the parts, how much of the entire energy remains? Answer, 25,659.8 pounds. 36. The energy of the steam in the steam cylinder is transmitted to the pump end or water cylinder by means of the piston rod. The piston rod enters both cylinders by means of stuffing boxes which are suitably packed to make them steam and water tight. The piston in the steam cylinder and the plunger in the water cylinder are securely fastened to their respective ends of the piston rod. Referring to example 4, the plunger of the pump has an area of 78.54 square inches. The total energy supplied it from the steam cylinder is 25,659.8 pounds. What pressure per square inch can be attained? Answer, 326.71- pounds. 37. The specific gravity of one grade of Pennsylvania crude oil is .886, or, in other words, 1 cubic foot of that grade weighs 886 ounces. How many pounds will a barrel of this oil weigh (a barrel contains 31.5 gallons)? Answer, 232.575 pounds. 38. One pound of this oil will evaporate 21.48 pounds of water from and at 212 F. How many pounds of water at that temperature will a barrel of the oil evaporate? Answer, 4,995.711 pounds. 39. A milling machine cutter has a circumference measuring 12.87 inches. If it makes 478.5 revolutions per minute, how many feet will a point on the circumference travel in one minute? Answer, 513.19 feet. 40. On a vessel having a crew of 460 officers and men, it was esti mated that each officer and man used 35.25 gallons of fresh water per day. What was the total number of ga lons used in one month of 30 days? Answer, 486,450 gallons. 41. Pure air is a mixture of oxygen and nitrogen in the following proportions: By volume, 2,091 parts oxygen to 7,909 parts nitrogen. By weight, 2,316 parts oxygen to 7,685 parts nitrogen. How many cubic feet oxygen are there in a space holding 250 cubic feet of air? Answer, 52.275 cubic feet. 42. How many cubic feet of nitrogen? Answer, 197.725 cubic feet. 43. The temperature of air in a room is 60° F. and the weight of 1 cubic foot of air at atmospheric pressure and 60° F. is .0764 pounds. How many pounds of air was in the room? (Example 41.) Answer, 19.1 pounds. 44. How many pounds of oxygen were in the room? Answer, 4.42356 pounds. How many pounds of nitrogen? Answer, 14.67835 pounds. 45. In the naval service the allowance of cooling surface of surface condensers varies from 1 to 1.25 square feet per I. H. P. for battleships and cruisers. In torpedo boats and torpedo-boat destroyers .85 square feet per I. H. P. What would be the cooling surface in square feet of a main condenser of a vessel whose I. H. P. is 9,450, the cooling surface allowed being 1.18 square feet per I. H. P.? Answer, 11,151 square feet. 46. What is the area in square feet of the cooling surface of a surface condenser on a torpedo boat whose I. H. P. is 5,240, allowing .9 square foot per I. H. P.? Answer, 4,716 square feet. 47. The linear expansion of cast steel is .00000636 of its length for each degree of F. rise in temperature. If the piston of a low pressure cylinder of an engine is 72 inches in diameter, at 32° F., what will be its diameter when the temperature is 257.5° F. (257.5° F. is the temperature corresponding to steam at 34 pounds per square inch, absolute.) Answer, 72.10326096 inches. 48. The linear expansion of cast iron for each degree F. rise in temperature is .00000556 of its length. What will be the diameter of a cast-iron piston whose diameter at 49° F. is 12 inches when it is heated to 450° F.? Answer, 12.02675472 inches. 49. A certain piece of machinery is made of Navy brass. This alloy is composed of .62 copper, .01 tin, and .37 zinc. The weight of the casting is 5,460 pounds. What is the weight of each of the above elements used in making the casting? Answer, copper 3,385.2 pounds, tin 54.6 pounds, zinc 2,020.2 pounds. DIVISION OF DECIMALS. XVI. Division of decimals is the process of finding the quotient of two numbers involving decimals. XVII. Placing the decimal point in the quotient depends on the following principle: The number of decimal orders in the quotient is equal to the number of decimal orders in the minuend, less the number in the divisor. Thus: Let .006 be divided by .03. The number of decimal places in the quotient will be 1. For .006 equals 100 and .93 equals 180. Then the quotient of .006 divided by .03 will be the same as 100 divided by 180 1800 180=10. Therefore, .006.03.2, in which there is one decimal order. XVIII. In division of decimals, to avoid making a mistake in the placing of the decimal point in the quotient, proceed as in the following example: Divide .09395 by 57. Solution. .00164+ 57). 09395 57 369 342 275 228 47 Explanation: Write the work in brief form as in the above example. Place the point for the quotient directly above that in the dividend. Place the quotient for each step of the work directly over last figure of the dividend used. As the first figure in the dividend is a cipher, we place a cipher over it and next to the decimal point. The next figure in the dividend being 9, is not divisible by 57, so we place another cipher over the 9 and to the right of the first cipher. The next figure of the dividend is 3, therefore we have 93. This can be divided by 57, so we place the quotient, which is 1, directly over the last figure of the dividend we are using (which in this case is 3). Subtract the 57 from the 93 and write the remainder, which is 36, directly below the 57. Continue the division as in whole numbers. The sign shows that the quotient is a little more than .00164. To six decimal places it is a little less than .00165, and if the quotient was carried further would be indicated by .00165-. XIX. Multiplying both dividend and divisor by the same number does not change the quotient. For instance, if we take the example" divide 50 by 10." the quotient will be 5. Now, if we multiply the dividend, 50, by 10, the product will be 500. Multiplying the divisor, 10, by 10, the product is 100. Dividing 500 by 100 the quotient is also 5. Suppose we take the example "divide 2.125 by .5." Applying the same principle 2. 125×10=21.25 NOTE.-Observe that the number of places in the quotient is equal to the number of places in the dividend less the number of places in the divisor. Example: Divide .05 by .005. Multiplying both dividend and divisor by 1,000 we have 50 divided by 5. Now, 50 divided by 5 equals 10 answer. Multiply the divisor by some number that will make it a whole number, and then multiply the dividend by the same number. Then proceed with the division. EXAMPLES. 1. Divide 1.125 by .03. Answer, 37.5. 5. Divide .96 by .24. Answer, 4. Answer, 50.004. 6. Divide .0425 by .0085. Answer, 5. 7. Divide 21 by .5. 8. Divide 2 by .008. 9. Divide 37.2 by 5. Answer, 42. 10. Divide 100.8788 by 454. Answer, .2222. 11. Divide .000343 by 3.43. Answer, .0001. Answer, 1.122. 12. Divide 9,811.0047 by .108649. Answer, 90,300. Answer, 1,000. Answer, .0265625. 27. Divide .0123 by 3.21. Answer, .00383177+. 28. An engine makes 3,947.52 revolutions of the shaft in 42.25 minutes. How many revolutions does it make per minute? Answer, 93.4+ revolutions. 29. There were 2,460.75 tons of coal taken on board the ship at Lisbon, Portugal, which cost $11,152.35. How much did the coal cost per ton? Answer, $4.53+. 30. 4.56 tons of coal were burned in 2.3 hours. How much coal was burned per hour? Answer, 1.983 tons. MISCELLANEOUS EXAMPLES. 1. What is the cost of 9 yards of flannel at $0.40 per yard and 12 yards at $0.75 per yard? Answer, $12.60. 2. What is the cost of 2.3 yards of toweling at $0.45 per yard and 1.5 yards at $0.375 per yard? Answer, $1.5975. 3. What is the cost of 16.25 yards of cloth at $2.6875 per yard? Answer, $43.671875. 4. At $0.75 per yard, how much cloth can be bought for $35.25? Answer, 47 yards. 5. At $2.5625 per gallon, how many gallons of varnish can be bought for $98.40? Answer, 38.4 gallons. 6. What will 6 hundredweight 50 pounds of boiler compound cost at $3.25 per hundredweight? Answer, $21.125. 7. What will 14 bushels 3 pecks 4 quarts of charcoal cost at $0.625 per bushel? Answer, $9.296875. 8. At $0.3125 per bushel, how much coke can be bought for $9.296875? Answer, 29 bushels 3 pecks. 9. If 63 gallons of oil cost $49, what will 464 gallons cost? Answer, $360.89. 10. Add .34 yard 1.07 feet 8.92 inches. Answer, 2 feet 10 inches. 11. Add .625 gallon, and .75 quart. Answer, 3 quarts .5 pints. 12. From 1.53 yards subtract 2 feet 3.08 inches. Answer, 2 feet 4 inches. 13. From .05 year subtract .2 hour. minutes. 14. From .41 day subtract .16 hour. 48 seconds. Answer, 18 days 5 hours 48 Answer, 9 hours 40 minutes. 15. Find the value of 3 year in integers. Answer, 109 days 13 hours 30 minutes. 16. What is the cost of 343 yards 2 feet 3 inches of tubing at $0.16 per yard? Answer, $55. 17. At $690.35 per mile, what is the cost of a road 17 miles and 135 rods long? Answer, $12,027.19140625. 18. In coaling a naval vessel the various methods of checking the amounts of coal is as follows: By tallying the bags and taking the average weight; by taking the draft of the ship before and after coaling; and by estimating the coal in the bunkers before and after coaling. In order to find the weight per cubic foot contained in the bunkers the coal is weighed in a box containing 16 cubic feet from time to time during the coaling. What is the density or weight of a cubic foot of a certain kind of coal in the above box if the box full weighs 808 pounds (work to nearest tenth)? Answer, 50.5 pounds. 19. The weight of a certain kind of metal per cubic foot is 486.6 pounds. How many cubic feet of the above metal will make a ton of 2,240 pounds? Answer, 4.6+ cubic feet. 20. If shovels are worth $0.85 apiece, how many can be bought for $22.10? Answer, 26 shovels. 21. A man earns $162 in 13.5 weeks. Answer, $12. What are his wages per week? 22. How long will it take a steam launch that has a speed of 6.75 miles per hour to travel 20.25 miles? Answer, 3 hours. 23. A cubic inch of cast-iron weighs .2607 pounds. How many cubic inches (to the nearest tenth) are there in a mass that weighs 10 pounds? Answer, 38.4 cubic inches. 24. Ice is .92 as heavy as water. Glass is 2.89 as heavy as water. How many times as heavy as ice is glass (answer to nearest hundredth)? Answer, 3.14 times. 25. How long will it take a ship making 18.87 knots to make a journey of 367.965 miles? Answer, 19.5 hours. 26. Divide .05 by .005. Answer, 10. 27. The heating surface of a boiler is 4685.1 square feet. The grate surface is 96.6 square feet. How many square feet of heating surface to a square foot of grate surface? Answer, 48.5 square feet. |