44376 16 App5a A63-A75
APPENDIXVMeasurementSECTIONV.1ObjectivesAmerican Units of MeasurementTwo common systems of measurement are the American (or English) system and themetric system. We will discuss American units of measurement in this section andmetric units in the next. Some common American units are inches, feet, miles, ounces,pounds, tons, cups, pints, quarts, and gallons. These units are used when measuringlength, weight, and capacity.1 Use a ruler to measure lengths in inches.A ruler is one of the most common tools used for measuring distances or lengths. Thefigure below shows part of a ruler. Most rulers are 12 inches (1 foot) long. Since12 inches 1 foot, a ruler is divided into 12 equal lengths of 1 inch. Each inch isdivided into halves of an inch, quarters of an inch, eighths of an inch, and sixteenthsof an inch.The left end of a ruler can be (but sometimes isn’t) labeled with a 0. Each pointon a ruler, like each point on a number line, has a number associated with it.Thatnumber is the distance between the point and 0. Several lengths on the ruler areshown below.1Use a ruler to measure lengthsin inches.2Define American units oflength.3Convert from one Americanunit of length to another.4Define American units ofweight.5Convert from one Americanunit of weight to another.6Define American units ofcapacity.7Convert from one Americanunit of capacity to another.8Define units of time.9Convert from one unit of timeto another.3 1– in.42 1– in.21 7– in.81 in.0123InchesActual sizeEXAMPLE 1Find the length of the paper clipshown here.Strategy We will place a ruler below the paper clip,with the left end of the ruler (which could be thought ofas 0) directly underneath one end of the paper clip.WHY Then we can find the length of the paper clip by identifying where its otherend lines up on the tick marks printed in black on the ruler.A-63
A-64Appendix V MeasurementSelf Check 1Find the length of the jumbopaper clip.Solution– in.138Since the tick marks between 0 and 1 on theruler create eight equal spaces, the ruler isscaled in eighths of an inch. The paper clip is1 38 inches long.8 spacesNow Try Problem 27Self Check 213– in.82InchesEXAMPLE 2Find the length of the nail shown below.Find the width of the circle.Strategy We will place a ruler below the nail, with the left end of the ruler (whichcould be thought of as 0) directly underneath the head of the nail.WHY Then we can find the length of the nail by identifying where its pointed endlines up on the tick marks printed in black on the ruler.SolutionNow Try Problem 29Since the tick marks between 0 and 1 on the ruler create sixteen equal spaces, theruler is scaled in sixteenths of an inch.72 –– in.1616 spaces127––in.163InchesThe nail is 2 167 inches long.2 Define American units of length.The American system of measurement uses the units of inch, foot, yard, and mile tomeasure length. These units are related in the following ways.American Units of Length1 foot (ft) 12 inches (in.)1 yard (yd) 36 inches1 yard 3 feet1 mile (mi) 5,280 feetThe abbreviation for each unit is written within parentheses.The Language of Mathematics According to some sources, the inch wasoriginally defined as the length from the tip of the thumb to the first knuckle.In some languages the word for inch is similar to or the same as thumb. Forexample, in Spanish, pulgada is inch and pulgar is thumb. In Swedish, tum isinch and tumme is thumb. In Italian, pollice is both inch and thumb.
V.1 American Units of Measurement3 Convert from one American unit of length to another.To convert from one unit of length to another, we use unit conversion factors. To findthe unit conversion factor between yards and feet, we begin with this fact:3 ft 1 ydIf we divide both sides of this equation by 1 yard, we get1 yd3 ft 1 yd1 yd3 ft 11 ydSimplify the right side of the equation. A number divided by itself is 1:1 yd1 yd 1.ftThe fraction 13 ydis called a unit conversion factor, because its value is 1. It can beread as “3 feet per yard.” Since this fraction is equal to 1, multiplying a length by thisfraction does not change its measure; it changes only the units of measure.To convert units of length in the American system of measurement, we use thefollowing unit conversion factors. Each conversion factor shown below is a form of 1.To convert fromUse the unitconversion factorTo convert fromfeet to inches12 in.1 ftinches to feetyards to feet3 ft1 ydfeet to yards1 ft12 in.1 yd3 ftyards to inches36 in.1 ydinches to yards1 yd36 in.5,280 ft1 mimiles to feetEXAMPLE 3feet to milesUse the unitconversion factor1 mi5,280 ftSelf Check 3Convert 8 yards to feet.Strategy We will multiply 8 yards by a carefully chosen unit conversion factor.WHY If we multiply by the proper unit conversion factor, we can eliminate theunwanted units of yards and convert to feet.SolutionTo convert from yards to feet, we must use a unit conversion factor that relatesfeet to yards. Since there are 3 feet per yard, we multiply 8 yards by the unitftconversion factor 13 yd.8 yd 8 yd1 .8 yd 3 ftⴢ11 ydWrite 8 yd as a fraction: 8 yd ftThen multiply by a form of 1: 31 yd.8 yd 3 ftⴢ11 ydRemove the common units of yards from the numeratorand denominator. Notice that the units of feet remain. 8 ⴢ 3 ftSimplify. 24 ftMultiply: 8 ⴢ 3 24.8 yards is equal to 24 feet.Success Tip Notice that in Example 3, we eliminated the units of yards andintroduced the units of feet by multiplying by the appropriate unit conversionfactor. In general, a unit conversion factor is a fraction with the following form:Unit we want to introduceUnit we want to eliminate䊴䊴NumeratorDenominatorConvert 9 yards to feet.Now Try Problem 35A-65
A-66Appendix V MeasurementSelf Check 4Convert 1 12 feet to inches.Now Try Problem 39EXAMPLE 43Convert 1 feet to inches.43Strategy We will multiply 1 feet by a carefully chosen unit conversion factor.4WHY If we multiply by the proper unit conversion factor, we can eliminate theunwanted units of feet and convert to inches.SolutionTo convert from feet to inches, we must choose a unit conversion factor whosenumerator contains the units we want to introduce (inches), and whosedenominator contains the units we want to eliminate (feet). Since there are12 inches per foot, we will use12 in.1 ft䊴䊴This is the unit we want to introduce.This is the unit we want to eliminate (the original unit).To perform the conversion, we multiply.312 in.71 ft ft #441 ft 712 in.ft ⴢ41 ft 7 # 12in.4#1Write 1 34 as an improper fraction: 1 34 47 .12 in.Then multiply by a form of 1: 1 ft .Remove the common units of feet from the numerator anddenominator. Notice that the units of inches remain.Multiply the fractions.17ⴢ3ⴢ4 in.4ⴢ1To simplify the fraction, factor 12. Then remove the commonfactor of 4 from the numerator and denominator. 21 in.Simplify.11 34feet is equal to 21 inches.Caution! When converting lengths, if no common units appear in thenumerator and denominator to remove, you have chosen the wrongconversion factor.Sometimes we must use two (or more) unit conversion factors to eliminate thegiven units while introducing the desired units. The following example illustrates thisconcept.Football A football field (including both end zones) is120 yards long. Convert this length to miles. Give the exact answer and a decimalapproximation, rounded to the nearest hundredth of a mile.10203040504030long-distance race with an officialdistance of 26 miles 385 yards.Convert 385 yards to miles.Give the exact answer and adecimal approximation, roundedto the nearest hundredth of amile.EXAMPLE 520MARATHONS The marathon is a10Self Check 5102030405040302010Now Try Problem 43120 yd
V.1 American Units of MeasurementStrategy We will use a two-part multiplication process that converts 120 yards tofeet and then converts that result to miles.WHY We must use a two-part process because the table on page 445 does notcontain a single unit conversion factor that converts from yards to miles.SolutionSince there are 3 feet per yard, we can convert 120 yards to feet by multiplying by3ftthe unit conversion factor 1yd. Since there is 1 mile for every 5,280 feet, we can1 miconvert that result to miles by multiplying by the unit conversion factor 5,280ft .120 yd 3 ft1 mi120 yd ⴢⴢ11 yd 5,280 ft120 yd 3 ft1 mi ⴢⴢ11 yd 5,280 ft 120 # 3mi5,28011Write 120 yd as a fraction: 120 yd ⴝ 1201 yd.Then multiply by two unit conversion3 ft1 mifactors: 1 yd 1 and 5,280 ft 1.Remove the common units of yards andfeet in the numerator and denominator.Notice that all the units are removedexcept for miles.Multiply the fractions.1112ⴢ2ⴢ2ⴢ3ⴢ5ⴢ3 mi2 ⴢ 2 ⴢ 2 ⴢ 2 ⴢ 2 ⴢ 3 ⴢ 5 ⴢ 11To simplify the fraction, prime factor120 and 5,280, and remove the commonfactors 2, 3, and 5.3 mi44Multiply the remainingfactors in the numerator.Multiply the remainingfactors in the denominator.111110.06844冄3.000 03 00 2 64360 35283A football field (including the end zones) is exactly 44miles long.We can also present this conversion as a decimal. If we divide3 by 44 (as shown on the right), and round the result to the nearesthundredth, we see that a football field (including the end zones) isapproximately 0.07 mile long.4 Define American units of weight.The American system of measurement uses the units of ounce, pound, and ton tomeasure weight. These units are related in the following ways.American Units of Weight1 pound (lb) 16 ounces (oz)1 ton (T) 2,000 poundsThe abbreviation for each unit is written within parentheses.5 Convert from one American unit of weight to another.To convert units of weight in the American system of measurement, we use thefollowing unit conversion factors. Each conversion factor shown below is a form of 1.To convertfrompounds to ouncestons to poundsUse the unitconversionfactor16 oz1 lb2,000 lb1 tonTo convertfromounces to poundspounds to tonsUse the unitconversionfactor1 lb16 oz1 ton2,000 lbA-67
A-68Appendix V MeasurementSelf Check 6EXAMPLE 6Convert 40 ounces to pounds.Convert 60 ounces topounds.Strategy We will multiply 40 ounces by a carefully chosen unit conversion factor.Now Try Problem 47WHY If we multiply by the proper unit conversion factor, we can eliminate theunwanted units of ounces and convert to pounds.SolutionTo convert from ounces to pounds, we must choose a unit conversion factor whosenumerator contains the units we want to introduce (pounds), and whosedenominator contains the units we want to eliminate (ounces). Since there is1 pound for every 16 ounces, we will use1 lb16 oz䊴䊴This is the unit we want to introduce.This is the unit we want to eliminate (the original unit).To perform the conversion, we multiply.40 oz 40 oz # 1 lb116 ozWrite 40 oz as a fraction: 40 oz 401 oz. Then multiply by a1 lbform of 1: 16 oz . 40 oz 1 lbⴢ116 ozRemove the common units of ounces from the numeratorand denominator. Notice that the units of pounds remain. 40lb16Multiply the fractions.There are two ways to complete the solution. First, we can remove any commonfactors of the numerator and denominator to simplify the fraction. Then we canwrite the result as a mixed number.15ⴢ81540lb lb lb 2 lb162ⴢ8221A second approach is to divide the numerator by the denominator and express theresult as a decimal.40lb 2.5 lb16Perform the division: 40 16.40 ounces is equal to 2 12 lb (or 2.5 lb).Self Check 7EXAMPLE 72.516冄40.0 3280 8 00Convert 25 pounds to ounces.Convert 60 pounds toounces.Strategy We will multiply 25 pounds by a carefully chosen unit conversion factor.Now Try Problem 51WHY If we multiply by the proper unit conversion factor, we can eliminate theunwanted units of pounds and convert to ounces.SolutionTo convert from pounds to ounces, we must chose a unit conversion factor whosenumerator contains the units we want to introduce (ounces), and whosedenominator contains the units we want to eliminate (pounds). Since there are16 ounces per pound, we will use16 oz1 lb䊴䊴This is the unit we want to introduce.This is the unit we want to eliminate (the original unit).
V.1 American Units of MeasurementTo perform the conversion, we multiply.25 lb 25 lb # 16 oz11 lbWrite 25 lb as a fraction: 25 lb ⴝ16 ozform of 1: 1 lb . 25 lb 16 ozⴢ11 lbRemove the common units of pounds from the numeratorand denominator. Notice that the units of ounces remain. 25 # 16 ozSimplify. 400 ozMultiply: 25 ⴢ 16 400.25 lb1 .Then multiply by a25 1615025040025 pounds is equal to 400 ounces.6 Define American units of capacity.The American system of measurement uses the units of ounce, cup, pint, quart, andgallon to measure capacity. These units are related as follows.The Language of MathematicsThe word capacity means the amount thatcan be contained. For example, a gas tank might have a capacity of 12 gallons.American Units of Capacity1 cup (c) 8 fluid ounces (fl oz)1 pint (pt) 2 cups1 quart (qt) 2 pints1 gallon (gal) 4 quartsThe abbreviation for each unit is written within parentheses.7 Convert from one American unit of capacity to another.To convert units of capacity in the American system of measurement, we use thefollowing unit conversion factors. Each conversion factor shown below is a form of 1.To convertfromcups to ouncesUse the unitconversionfactor8 fl oz1cTo convertfromounces to cupsUse the unitconversionfactor1c8 fl ozpints to cups2c1 ptcups to pints1 pt2cquarts to pints2 pt1 qtpints to quarts1 qt2 ptgallons to quarts4 qt1 galquarts to gallons1 gal4 qtA-69
A-70Appendix V MeasurementSelf Check 8EXAMPLE 8Cooking If a recipe calls for 3 pints of milk, how manyfluid ounces of milk should be used?Convert 2.5 pints to fluidounces.Strategy We will use a two-part multiplication process that converts 3 pints tocups and then converts that result to fluid ounces.Now Try Problem 55WHY We must use a two-part process because the table on page A-69 does notcontain a single unit conversion factor that converts from pints to fluid ounces.SolutionSince there are 2 cups per pint, we can convert 3 pints to cups by multiplying by theunit conversion factor 12ptc . Since there are 8 fluid ounces per cup, we can convertthat result to fluid ounces by multiplying by the unit conversion factor 8 1fl coz.3 ptWrite 3 pt as a fraction: 3 pt ⴝ 1 .Multiply by two unit conversion factors:2c8 fl oz1 pt ⴝ 1 and 1 c ⴝ 1. Felix Wirth/Corbis3 pt 2 c 8 fl oz# #3 pt 1 1 pt 1 c Remove the common units of pints and cups inthe numerator and denominator. Notice that allthe units are removed except for fluid ounces.3 pt 2 c 8 fl ozⴢⴢ11 pt1c 3 # 2 # 8 fl ozSimplify. 48 fl ozMultiply.Since 3 pints is equal to 48 fluid ounces, 48 fluid ounces of milk should be used.8 Define units of time.The American system of measurement (and the metric system) uses the units ofsecond, minute, hour, and day to measure time. These units are related as follows.Units of Time1 minute (min) 60 seconds (sec)1 hour (hr) 60 minutes1 day 24 hoursThe abbreviation for each unit is written within parentheses.To convert units of time, we use the following unit conversion factors. Eachconversion factor shown below is a form of 1.To convertfromUse the unitconversionfactorTo convertfromUse the unitconversionfactorminutes to seconds60 sec1 minseconds to minutes1 min60 sechours to minutes60 min1 hrminutes to hours1 hr60 mindays to hours24 hr1 dayhours to days1 day24 hr
V.1 American Units of Measurement9 Convert from one unit of time to another.EXAMPLE 9AstronomyA lunar eclipse occurs when the Earth isbetween the sun and the moon in such a way that Earth’s shadow darkens themoon. (See the figure below, which is not to scale.) A total lunar eclipse can last aslong as 105 minutes. Express this time in hours.Self Check 9THE SUN A solar eclipse (eclipseof the sun) can last as long as450 seconds. Express this timein minutes.Now Try Problem 59SunEarthMoonStrategy We will multiply 105 minutes by a carefully chosen unit conversionfactor.WHY If we multiply by the proper unit conversion factor, we can eliminate theunwanted units of minutes and convert to hours.SolutionTo convert from minutes to hours, we must choose a unit conversion factor whosenumerator contains the units we want to introduce (hours), and whosedenominator contains the units we want to eliminate (minutes). Since there is1 hour for every 60 minutes, we will use1 hr60 minThis is the unit we want to introduce.This is the unit we want to eliminate (the original unit).䊴䊴To perform the conversion, we multiply.105 min 105 min # 1 hr160 minWrite 105 min as a fraction: 105 ⴝThen multiply by a form of 1: 601 hrmin . 105 min # 1 hr160 minRemove the common units of minutes in the numeratorand denominator. Notice that the units of hours remain. 105hr60Multiply the fractions.11105 min.13ⴢ5ⴢ7 hr2ⴢ2ⴢ3ⴢ5To simplify the fraction, prime factor 105 and 60.Then remove the common factors 3 and 5 in thenumerator and denominator.7 hr4Multiply the remaining factors in the numerator.Multiply the remaining factors in the denominator. 1 34 hrWrite 47 as a mixed number.11A total lunar eclipse can last as long as 1 34 hours.ANSWERS TO SELF CHECKS1. 1 78 in. 2. 1 14 in. 3. 27 ft 4. 18 in.7. 960 oz 8. 40 fl oz 9. 7 12 min5.732mi 0.22 mi6. 3 34 lb 3.75 lbA-71
A-72Appendix V MeasurementSECTIONV.1STUDY SETVO C AB UL ARY15. Write a unit conversion factor to converta. pounds to tonsFill in the blanks.1. A ruler is used for measuringb. quarts to pints.2. Inches, feet, and miles are examples of Americanunits of3.a. inches to yards3 ft 1 ton4 qt1 yd , 2,000 lb , and 1 galare examples ofconversionfactors.b. days to minutes17. Match each item with its proper measurement.4. Ounces, pounds, and tons are examples of Americanunits of.a. Length of theU.S. coastline5. Some examples of American units ofarecups, pints, quarts, and gallons.6. Some units ofb. Height of aBarbie dollare seconds, minutes, hours, anddays.c. Span of the Golden1i. 112 in.ii. 4,200 ftiii. 53.5 ydiv. 12,383 miGate BridgeCONCEPTSd. Width of a footballfieldFill in the blanks.7. a. 12 inches b.16. Write the two unit conversion factors used to convert18. Match each item with its proper measurement.foota. Weight of the men’sfeet 1 yardc. 1 yard inchesd. 1 mile shot put used in trackand fieldfeetb. Weight of an African8. a.ounces 1 poundb.pounds 1 ton9. a. 1 cup b. 1 pint c. 2 pints 10. a. 1 day is worth 50019. Match each item with its proper measurement.quarta. Amount of bloodin an adultgallonb. Size of the Exxonhoursminutes11. The value of any unit conversion factor is.12. In general, a unit conversion factor is a fraction withthe following form:Unit that we want toUnit that we want to13. Consider the work shown below.48 oz 1 lbⴢ116 oza. What units can be removed?b. What units remain?14. Consider the work shown below.600 yd 3 ft1 miⴢⴢ11 yd 5,280 fta. What units can be removed?b. What units remain?iii. 7.2 tonsc. Amount of gold thatcupsb. 2 hours ii. 16 lbelephantfluid ouncesd. 4 quarts i. 112 ozValdez oil spill in1989i.12fluid ozii. 2 cupsiii. 5 qtiv. 10,080,000 galc. Amount of nail polishin a bottled. Amount of flour to䊴䊴NumeratorDenominatormake 3 dozen cookies20. Match each item with its proper measurement.a. Length of firstU.S. manned spaceflightb. A leap yearc. Time differencebetween New Yorkand Fairbanks, Alaskad. Length of WrightBrothers’ first flighti. 12 secii. 15 miniii. 4 hriv. 366 days
A-73V.1 American Units of Measurement28. Find the length of the needle.NOTATION21. What unit does each abbreviation represent?a. lbb. ozc. fl oz122. What unit does each abbreviation represent?a. qt23Inchesb. cc. ptRefer to the given ruler to answer each question. See Example 2.Complete each solution.29. a. Each inch is divided into how many equalparts?23. Convert 2 yards to inches.2 yd b. Determine which measurements the arrows point2 ydin.ⴢ11 ydto on the ruler. 2 ⴢ 36 in.24. Convert 24 pints to quarts.24 pt 24 pt 1 qtⴢ1pt1323Inches24 1 ⴢ1 2 230. Find the length of the bolt.qt25. Convert 1 ton to ounces.1 ton lboz1 tonⴢⴢ11 ton1 lb 1 ⴢ 2,000 ⴢ 16 1ozInches26. Convert 37,440 minutes to days.1 day1 hrⴢminhr37,440 min 37,440 min ⴢ Use a ruler scaled in sixteenths of an inch to measure eachobject. See Example 2.37,44060 ⴢ 24 31. The width of a dollar billdays32. The length of a dollar bill33. The length (top to bottom) of this pageGUIDED PR AC TICERefer to the given ruler to answer each question. See Example 1.34. The length of the word as printed here:supercalifragilisticexpialidocious27. a. Each inch is divided into how many equal parts?b. Determine which measurements the arrows pointto on the ruler.Perform each conversion. See Example 3.35. 4 yards to feet36. 6 yards to feet37. 35 yards to feet38. 33 yards to feetPerform each conversion. See Example 4.1Inches23231240. 2 feet to inches1442. 6 feet to inches39. 3 feet to inches41. 5 feet to inches12
A-74Appendix V MeasurementUse two unit conversion factors to perform each conversion.Give the exact answer and a decimal approximation, rounded tothe nearest hundredth, when necessary. See Example 5.TRY IT YO URSELFPerform each conversion.63. 3 quarts to pints64. 20 quarts to gallons65. 7,200 minutes to days66. 691,200 seconds to days67. 56 inches to feet68. 44 inches to feet69. 4 feet to inches70. 7 feet to inches71. 16 pints to gallons72. 3 gallons to fluid ouncesPerform each conversion. See Example 6.73. 80 ounces to pounds74. 8 pounds to ounces47. Convert 44 ounces to pounds.75. 240 minutes to hours76. 2,400 seconds to hours48. Convert 24 ounces to pounds.77. 8 yards to inches78. 324 inches to yards79. 90 inches to yards80. 12 yards to inches81. 5 yards to feet82. 21 feet to yards83. 12.4 tons to pounds84. 48,000 ounces to tons85. 7 feet to yards86. 423 yards to feet87. 15,840 feet to miles88. 2 miles to feet43. 105 yards to miles44. 198 yards to miles45. 1,540 yards to miles46. 1,512 yards to miles49. Convert 72 ounces to pounds.50. Convert 76 ounces to pounds.Perform each conversion. See Example 7.51. 50 pounds to ounces52. 30 pounds to ounces53. 87 pounds to ounces54. 79 pounds to ounces89.12mile to feet90. 1,320 feet to milesPerform each conversion. See Example 8.91. 7,000 pounds to tons92. 2.5 tons to ounces55. 8 pints to fluid ounces93. 32 fluid ounces to pints 94. 2 quarts to fluid ounces56. 5 pints to fluid ounces57. 21 pints to fluid ounces58. 30 pints to fluid ouncesPerform each conversion. See Example 9.59. 165 minutes to hours60. 195 minutes to hoursA P P L I C ATI O N S95. THE GREAT PYRAMID The Great Pyramid inEgypt is about 450 feet high. Express this distance inyards.96. THE WRIGHT BROTHERS In 1903, OrvilleWright made the world’s first sustained flight. Itlasted 12 seconds, and the plane traveled 120 feet.Express the length of the flight in yards.62. 80 minutes to hoursHulton Archive/Getty Images61. 330 minutes to hours
V.1 American Units of Measurement97. THE GREAT SPHINX The Great Sphinx of Egyptis 240 feet long. Express this in inches.A-75108. CATERING How many cups of apple cider arethere in a 10-gallon container of cider?98. HOOVER DAM The Hoover Dam in Nevada is726 feet high. Express this distance in inches.99. THE SEARS TOWER The Sears Tower in Chicagohas 110 stories and is 1,454 feet tall. To the nearesthundredth, express this height in miles.100. NFL RECORDS Emmit Smith, the former DallasCowboys and Arizona Cardinals running back, holdsthe National Football League record for yardsrushing in a career: 18,355. How many miles is this?Round to the nearest tenth of a mile.101. NFL RECORDS When Dan Marino of the MiamiDolphins retired, it was noted that Marino’s careerpassing total was nearly 35 miles! How many yardsis this?109. SCHOOL LUNCHES Each student attendingEagle River Elementary School receives 1 pintof milk for lunch each day. If 575 students attendthe school, how many gallons of milk are usedeach day?110. RADIATORS The radiator capacity of a piece ofearth-moving equipment is 39 quarts. If the radiatoris drained and new coolant put in, how many gallonsof new coolant will be used?111. CAMPING Howmany ounces ofcamping stove fuelwill fit in thecontainer shown?FUEL12 –2 gal102. LEWIS AND CLARK The trail traveled by theLewis and Clark expedition is shown below. When theexpedition reached the Pacific Ocean, Clark estimatedthat they had traveled 4,162 miles. (It was laterdetermined that his guess was within 40 miles of theactual distance.) Express Clark’s estimate of thedistance in feet.WASHINGTONOREGONSOUTH DAKOTAIDAHOIOWANEBRASKAKANSAS155 minutes. To the nearest tenth, how many hoursdoes he walk?113. SPACE TRAVEL The astronauts of the Apollo 8mission, which was launched on December 21, 1968,were in space for 147 hours. How many days did themission take?114. AMELIA EARHART In 1935, Amelia EarhartNORTH DAKOTAMONTANAWYOMING112. HIKING A college student walks 11 miles inMISSOURIbecame the first woman to fly across the AtlanticOcean alone, establishing a new record for thecrossing: 13 hours and 30 minutes. How manyminutes is this?WRITING115. a. Explain how to find the unit conversion factorthat will convert feet to inches.103. WEIGHT OF WATER One gallon of water weighsabout 8 pounds. Express this weight in ounces.104. WEIGHT OF A BABY A newborn baby boyweighed 136 ounces. Express this weight inpounds.105. HIPPOS An adult hippopotamus can weigh asmuch as 9,900 pounds. Express this weight in tons.b. Explain how to find the unit conversion factorthat will convert pints to gallons.1 lb116. Explain why the unit conversion factor 16oz is a formof 1.REVIEW117. Round 3,673.263 to thea. nearest hundred106. ELEPHANTS An adult elephant can consume asmuch as 495 pounds of grass and leaves in one day.How many ounces is this?107. BUYING PAINT A painter estimates that he willneed 17 gallons of paint for a job. To take advantageof a closeout sale on quart cans, he decides to buythe paint in quarts. How many cans will he need tobuy?b. nearest tenc. nearest hundredthd. nearest tenth118. Round 0.100602 to thea. nearest thousandthb. nearest hundredthc. nearest tenthd. nearest one
A-76Appendix V MeasurementSECTIONObjectives1Define metric units of length.2Use a metric ruler to measurelengths.3Use unit conversion factors toconvert metric units of length.4Use a conversion chart toconvert metric units of length.5Define metric units of mass.6Convert from one metric unitof mass to another.7Define metric units of capacity.8Convert from one metric unitof capacity to another.9Define a cubic centimeter.V.2Metric Units of MeasurementThe metric system is the system of measurement used by most countries in the world.All countries, including the United States, use it for scientific purposes. The metricsystem, like our decimal numeration system, is based on the number 10. For this reason,converting from one metric unit to another is easier than with the American system.1 Define metric units of length.The basic metric unit of length is the meter (m). One meter is approximately 39 inches,which is slightly more than 1 yard.The figure below compares the length of a yardstickto a meterstick.1 yard:36 inches1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 361 meter:about 39 inches102030405060708090100Longer and shorter metric units of length are created by adding prefixes to thefront of the basic unit, meter.kilo means thousandsdeci means tenthshecto means hundredscenti means hundredthsdeka means tensmilli means thousandthsMetric Units of rs1meteror 0.1of a meteror 0.01of a or 0.001of a metermmThe Language of Mathematics It is helpful to memorize the prefixes listedabove because they are also used with metric units of weight and capacity.The most often used metric units of length are kilometers, meters, centimeters,and millimeters. It is important that you gain a practical understanding of metriclengths just as you have for the length of an inch, a foot, and a mile. Some examples ofmetric lengths are shown below.1m1 cm1 kilometer is about thelength of 60 train cars.1 meter is aboutthe distance from adoorknob to the floor.1 centimeter is aboutas wide as the nail onyour little finger.1 mm1 millimeter is aboutthe thicknessof a dime.
V.2 Metric Units of Measurement2 Use a metric ruler to measure lengths.Parts of a metric ruler, scaled in centimeters, and a ruler scaled in inches are shownbelow. Several lengths on the metric ruler are highlighted.53 mm2.54 cm 1 in.1 cmMetric system1Centimeters2345678910American system123Inches(Actual size)EXAMPLE 1Self Check 1Find the length of the nail shown below.To the nearest centimeter, findthe width of the circle.Strategy We will place a metric ruler below the nail, with the left end of the ruler(which could be thought of as 0) directly underneath the head of the nail.WHY Then we can find the length of the nail by identifying where its pointed endlines up on the tick marks printed in black on the ruler.SolutionThe longest tick marks on the ruler (those labeled with numbers) mark lengths incentimeters. Since the pointed end of the nail lines up on 6, the nail is 6 centimeterslong.123456Now Try Problem 237CentimetersEXAMPLE 2Find the length of the paper clip shown below.Self Check 2Find the length of the jumbopaper clip.Strategy We will place a metric ruler below the paper clip, with the left end of theruler (which could be thought of as 0) directly underneath one end of the paperclip.WHY Then we can find the length of the paper clip by identifying where its otherend lines up on the tick marks printed in black on the ruler.Now Try Problem 25A-77
A-78Appendix V MeasurementSolutionOn the ruler, the shorter tick marks divide each centimeter into 10 millimeters, asshown. If we begin at the left end of the ruler and count by tens as we move rightto 3, and then add an additional 6 millimeters to that result, we find that the lengthof the paper clip is 30 6 36 millimeters.10 mm110 mm210 mm36 mm456Centimeters3 Use unit conversion factors to convert metric units of length.Metric units of len
3 ft 1 yd 3 V.1 American Units of Measurement A-65 Self Check 3 Convert 9 yards to feet. Now Try Problem 35 Use the unit Use the unit To convert from conversion factor To convert from conversion factor feet to inches inches to feet yards to feet feet to yards yards to inches inches to yards miles to feet feet to miles 1 mi
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Electrical engineering 101 : everything you should have learned in school . . . but probably didn’t / Darren Ashby. p. cm. Includes index. ISBN 978-1-85617-506-7 (alk. paper) 1. Electric engineering. I. Title. TK146.A75 2009 621.3—dc22 2008045182 British Library Cataloguing-in-Publication Data
prefazione di Corrado Ricci Milano, Bestetti e Tvmminelli [1914] xx NA1119.S5A7 The Architectural sketch-book [Boston, J.R. Osgood & Co.], 1873-1876 NA1 .A75 L'architecture & la sculpture à l'Exposition de 1900 Paris, A. Guérinet [1904] x NA6750.P4A9 L'Architecture e
contactor Contactor number price Accessories for A/AF/AL & AE contactors Discount schedule ABA [OF] 1 Use type VE 5-2 for mechanical and electrical interlocking between A30/A40 and A50 - A75 contactors. Interlocks for two horizontally mounted contactors – AF1350 - AF2050 contactors
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First aiders must complete a training course approved by the Health and Safety Executive (HSE). 20 At school, the main duties of a first aider are to: give immediate help to casualties with common injuries or illnesses and those arising from specific hazards at school; when necessary, ensure that an ambulance or other professional medical help is called. PERSON? WHAT IS AN APPOINTED . 21 An .
