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Measurement NOTES

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Measurement NOTES

1. 1. Standards of MeasurementStandards of MeasurementUsing a measuring tool to compare some dimension ofUsing a measuring tool to compare some dimension ofan object to a standard.an object to a standard.For example, at one time theFor example, at one time thestandard for length was thestandard for length was theking’s foot. What are someking’s foot. What are someproblems with this standard?problems with this standard?
2. 2. WHO CARES ABOUT MEASUREMENT?!SCENARIOS:1. Your friends ask you to go somewhere…2.You want to go somewhere with your car…3. You’re sick…4.You’re hungry…5.Buying a new outfit?6.The sports field…7.You start school at 7:45am but you’re leaving fromyour friends house…8.A tree falls on the road… can you lift it?9.You’re vacationing and your plane must take off…
3. 3. UNITS OF MEASUREMENTUNITS OF MEASUREMENTUse SI units — based on the metricsystemLengthMassVolumeTimeTemperature
4. 4. Types of Observations andTypes of Observations andMeasurementsMeasurementsQUALITATIVEQUALITATIVE——changes in color andchanges in color andphysical state.physical state.QUANTITATIVE MEASUREMENTSQUANTITATIVE MEASUREMENTS------involveinvolve numbersnumbers◦ UseUse SI unitsSI units — based on the— based on themetric systemmetric system
5. 5. Stating a MeasurementStating a MeasurementIn every measurement there is aIn every measurement there is a♦NumberNumber followed by a…followed by a…♦ UnitUnit from a measuring devicefrom a measuring deviceThe number should also be asThe number should also be as preciseprecise as theas themeasurement!measurement!
6. 6. Some Tools for MeasurementSome Tools for MeasurementWhich tool(s)Which tool(s)would you use towould you use tomeasure:measure:A.A. temperaturetemperatureB.B. volumevolumeC.C. timetimeD.D. weightweight
7. 7. How many stars are in the Universe?300 Sextillion Stars
8. 8. What is Scientific Notation?What is Scientific Notation?Scientific notation = expressing really bigScientific notation = expressing really bignumbers or really small numbers…numbers or really small numbers…IN A CONCISE WAY!IN A CONCISE WAY!
9. 9. Scientific notation consists ofScientific notation consists oftwo parts:two parts:1. A number between 1 and 101. A number between 1 and 102.2.A power ofA power of 1010N x 10N x 10xx
10. 10. To change standard form toTo change standard form toscientific notation…scientific notation…1.1. Place the decimal point so that there is one non-zeroPlace the decimal point so that there is one non-zerodigit to the left of the decimal point.digit to the left of the decimal point.2.2. Count the number of decimal places the decimalCount the number of decimal places the decimalpoint has “moved” from the original number. Thispoint has “moved” from the original number. Thiswill be the exponent of the 10.will be the exponent of the 10.33. If original number is less than 1 = negative exponent. If original number is less than 1 = negative exponentIf the original number is > 1 = positive exponentIf the original number is > 1 = positive exponent
11. 11. ExamplesExamplesGiven: 289,800,000Given: 289,800,0002.8989 x 109Given: 0.000567Given: 0.0005675.67 x 10-4
12. 12. To change scientific notationTo change scientific notationto standard form…to standard form…Simply move the decimal point to the rightSimply move the decimal point to the rightfor positive exponent 10.for positive exponent 10.Move the decimal point to the left forMove the decimal point to the left fornegative exponent 10.negative exponent 10.(Use zeros to fill in places.)(Use zeros to fill in places.)
13. 13. ExampleExampleGiven: 5.093 x 10Given: 5.093 x 10665,093,0005,093,000Given: 1.976 x 10Given: 1.976 x 10-4-40.00019760.0001976
14. 14. Warm-Up: Express these numbers in ScientificExpress these numbers in ScientificNotation:Notation:1)1) 4057894057892)2) 0.0038720.0038723)3) 300000000030000000004)4) 22
15. 15. Metric PrefixesMetric Prefixes
16. 16. Metric PrefixesMetric PrefixesKilo-Kilo- means 1000 of that unitmeans 1000 of that unit◦ 1 kilometer (km) = 1000 meters (m)1 kilometer (km) = 1000 meters (m)Centi-Centi- means 1/100 of that unitmeans 1/100 of that unit◦ 1 meter (m) = 100 centimeters (cm)1 meter (m) = 100 centimeters (cm)Milli-Milli- means 1/1000 of that unitmeans 1/1000 of that unit◦ 1 Liter (L) = 1000 milliliters (mL)1 Liter (L) = 1000 milliliters (mL)
17. 17. Metric Conversions“King Henry Died by Drinking ChocolateMilk”K H D b D C M1) 2400 g = _____ kg2) 0.24 L = _____ mL3) 0.3 hm = _____ m4) 0.10 ms = _____ sec
18. 18. Learning Check1. 1000 m = 11. 1000 m = 1 ______ a) mm b) km c) dma) mm b) km c) dm2. 0.001 g = 12. 0.001 g = 1 ______ a) mg b) kg c) dga) mg b) kg c) dg3. 0.1 L = 13. 0.1 L = 1 ______ a) mL b) cL c) dLa) mL b) cL c) dL4. 0.01 m = 1 ___4. 0.01 m = 1 ___ a) mm b) cm c) dma) mm b) cm c) dm
19. 19. Reading a Meter stickReading a Meter stickFirst digit (known)First digit (known) ==Second digit (known)Second digit (known) ==Third digit (estimated) =Third digit (estimated) =Length reportedLength reported ==
20. 20. Known + Estimated DigitsKnown + Estimated Digits• Known digitsKnown digits are 100% certain!are 100% certain!• The third digit is estimated (uncertain)The third digit is estimated (uncertain)• In the reported length, all three digits (ex. =In the reported length, all three digits (ex. =2.75 cm) are significant2.75 cm) are significant includingincluding thetheestimated one.estimated one.CERTAIN + ESTIMATED = Significant Digits!CERTAIN + ESTIMATED = Significant Digits!
21. 21. Learning CheckLearning CheckWhat is the length of the line?What is the length of the line?How does your answer compare with yourHow does your answer compare with yourneighbor’s answer? Why or why not?neighbor’s answer? Why or why not?
22. 22. Measuring VolumeMake sureyou’re at eyelevel.Takemeasurement atthe bottom ofthe concavemeniscus.
23. 23. Always estimateAlways estimate ONEONE place past the smallest mark!place past the smallest mark!
24. 24. Three targetsThree targetswith threewith threearrows each toarrows each toshoot.shoot.Can you hit the bulls-eye?Can you hit the bulls-eye?Can you define accuracy and precision?Can you define accuracy and precision?
25. 25. Accuracy Vs. PrecisionAccuracy:How close a measured value is to the accepted/truevalue.Precision:How close a series of measurements are to one another.◦ Note: they may NOT be accurate
26. 26. Conversion FactorsExpresses an equal quantity of one unit toanother.1 in. = 2.54 cm or 1 inch per 2.54 cm.: 1 in. and 2.54 cm2.54 cm 1 in.EXAMPLE: How many students are in thisclass?
27. 27. Learning CheckWrite conversion factors that relate each ofWrite conversion factors that relate each ofthe following pairs of units:the following pairs of units:1. Liters and mL1. Liters and mL2. Hours and minutes2. Hours and minutes3. Meters and kilometers3. Meters and kilometers
28. 28. How many minutes are in 2.5 hours?Dimensional Analysis
29. 29. Sample ProblemIf you have lived for 52,200 hours, howIf you have lived for 52,200 hours, howlong were you alive in years? (Rememberlong were you alive in years? (RememberSIG FIGS!)SIG FIGS!)
30. 30. Learning CheckLearning CheckAn adult human has 4.65 L of blood. How manyAn adult human has 4.65 L of blood. How manygallons of blood is that?gallons of blood is that?Unit plan L qt gallonEqualities:1.06 qt = 1.0 L1 gallon = 4 quartsSetup:
31. 31. You Try This One!You Try This One!If Jacob stands on Spencer’sIf Jacob stands on Spencer’sshoulders, they are two and ashoulders, they are two and ahalf yards high. How manyhalf yards high. How manyinches is that?inches is that?
32. 32. Learning CheckHow many seconds are in 1.4 days?Unit plan: days hr min seconds
33. 33. Wait a minute!What isWhat is wrongwrong with the following setup?with the following setup?1.4 day x1.4 day x 1 day1 day xx 60 min60 min xx 60 sec60 sec24 hr 1 hr 1 min24 hr 1 hr 1 min
34. 34. Dealing with Two UnitsIf your pace on a treadmill is 65 meters perIf your pace on a treadmill is 65 meters perminute, what is your speed in miles perminute, what is your speed in miles perhour?hour?
35. 35. Sample ProblemThe United States uses 18,000,000 gallons of gasolineper day. How many liters are used each minute?
36. 36. Sample ProblemPotatoes sell 5 dollars for a 10 pound bag. How muchdoes one gram of potatoes cost?
37. 37. What about Square and Cubic units? Cubed Unit = CUBED NUMBER!Cubed Unit = CUBED NUMBER! Best way: Square or cube the ENTIREBest way: Square or cube the ENTIREconversion factor.conversion factor. Example: Convert 4.3 cmExample: Convert 4.3 cm33to mmto mm33
38. 38. Learning CheckLearning CheckA Nalgene waterA Nalgene waterbottle holds 1000bottle holds 1000cmcm33of dihydrogenof dihydrogenmonoxide. Howmonoxide. Howmany cubic metersmany cubic metersis that?is that?
39. 39. SolutionSolution1000 cm1000 cm33
40. 40. Significant Figures• The numbers reported in a measurementare limited by the measuring tool.• Significant figures• All KNOWN Digits• One ESTIMATED Digit
41. 41. Counting Significant FiguresRULE 1. All non-zero digits in a measured number aresignificant.Sig Figs38.15 cm ___5.6 ft ___65.6 lb ___122.55 m ___
42. 42. Leading ZerosRULE 2. Leading zeros in decimal numbers areNOT significant.Sig Figs0.008 mm ____0.0156 oz ____0.0042 lb ____0.000262 mL ____
43. 43. Sandwiched ZerosRULE 3. Zeros between nonzero numbers aresignificant.Sig Figs50.8 mm _____2001 min _____0.702 lb _____0.00405 m _____
44. 44. Trailing ZerosRULE 4. Trailing zeros in numbers withoutdecimals are NOT significant. Any final zero usedafter a decimal point is significant.Sig Figs25,000 in. ____200.30 yr ____4.320 gal ____25,005,000 g ____
45. 45. Learning CheckIn which set(s) do both numbers containthe same number of significant figures?1) 22.0 and 22.002) 400.0 and 403) 0.000015 and 150,000
46. 46. Learning CheckLearning CheckState the number of significant figures in each of theState the number of significant figures in each of thefollowing:following:A. 0.030 mA. 0.030 m ______________B. 4.050 LB. 4.050 L ______________C. 0.0008 gC. 0.0008 g ______________D. 3.00 mD. 3.00 m ______________E. 2,080,000 beesE. 2,080,000 bees ______________
47. 47. Rounding Significant Figures1) Round 2.0345 g to 3 sig figs.2) Round 0.000455 to 2 sig figs.
48. 48. Learning CheckA. Which answers contain 3 significant figures?1) 0.4760 2) 0.00476 3) 4760B. All the zeros are significant in1) 0.00307 2) 25.300 3) 2.050 x 103C. 534,675 rounded to 3 significant figures is1) 535 2) 535,000 3) 5.35 x 105
49. 49. Significant Numbers in Calculations• A calculated answer cannot be moreprecise than the measuring tool.• A calculated answer must match theleast precise measurement.
50. 50. Adding and SubtractingThe answer = same number of decimal places asthe measurement with the fewest decimal places.25.2 one decimal place+ 1.34 two decimal places26.54answer 26.5 (rounded to one decimal place)
51. 51. Learning CheckIn each calculation, round the answer to theIn each calculation, round the answer to thecorrect number of sig figs.correct number of sig figs.A. 235.05 + 19.6 + 2.1 =A. 235.05 + 19.6 + 2.1 =1) 256.751) 256.75 2) 256.82) 256.8 3) 2573) 257B. 58.925 - 18.2B. 58.925 - 18.2 ==1) 40.7251) 40.725 2) 40.732) 40.73 3) 40.73) 40.7
52. 52. Multiplying and DividingAnswer = the same number of significantfigures as the measurement with thefewest significant figures.What’s wrong with this answer?28.2 x 3.5 = 98.7
53. 53. Learning CheckLearning CheckA. 2.19 x 4.2 =A. 2.19 x 4.2 =1) 91) 9 2) 9.22) 9.2 3) 9.1983) 9.198B. 4.311 ÷ 0.07 =B. 4.311 ÷ 0.07 =1)1)61.5861.58 2) 622) 62 3) 603) 60C.C. (2.54 x 0.0028) =(2.54 x 0.0028) =(0.0105 x 0.060)(0.0105 x 0.060)1) 11.31) 11.3 2) 112) 11 3) 0.0413) 0.041
54. 54. DENSITYDENSITY - an important and useful- an important and usefulphysical propertyphysical propertyDensity = mass (g)volume (cm3)Density = mass (g)volume (cm3)Mercury13.6 g/cm13.6 g/cm3321.5 g/cm21.5 g/cm33Aluminum2.7 g/cm2.7 g/cm33Platinum
55. 55. ProblemProblem A piece of copper has a mass ofA piece of copper has a mass of57.54 g. It is 9.36 cm long, 7.23 cm wide,57.54 g. It is 9.36 cm long, 7.23 cm wide,and 0.95 mm thick. Calculate densityand 0.95 mm thick. Calculate density(g/cm(g/cm33).).Density = mass (g)volume (cm3)Density = mass (g)volume (cm3)
56. 56. StrategyStrategy1. Get dimensions in common units.1. Get dimensions in common units.2.2. Calculate volume in cubic centimeters.Calculate volume in cubic centimeters.3. Calculate the density.3. Calculate the density.
57. 57. SOLUTIONSOLUTION1. Get dimensions in common units.1. Get dimensions in common units.2.2. Calculate volume in cubic centimeters.Calculate volume in cubic centimeters.3. Calculate the density.3. Calculate the density.0.95 mm •1cm10 mm= 0.095 cm57.54 g6.4 cm3= 9.0 g/ cm3(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm33Note only 2 significant figures in the answer!Note only 2 significant figures in the answer!
58. 58. PROBLEM: Mercury (Hg) has a density of 13.6PROBLEM: Mercury (Hg) has a density of 13.6g/cmg/cm33. What is the mass of 95 mL of Hg in grams?. What is the mass of 95 mL of Hg in grams?In pounds?In pounds?PROBLEM: Mercury (Hg) has a density of 13.6PROBLEM: Mercury (Hg) has a density of 13.6g/cmg/cm33. What is the mass of 95 mL of Hg in grams?. What is the mass of 95 mL of Hg in grams?In pounds?In pounds?
59. 59. PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33..What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33..What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?StrategyStrategy1.1. Use density to calc. mass (g) fromUse density to calc. mass (g) from volume.volume.2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)Need to know conversion factorNeed to know conversion factor= 454 g / 1 lb= 454 g / 1 lbFirst, note thatFirst, note that 1 cm1 cm33= 1 mL= 1 mL
60. 60. PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33..What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33..What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?1.1. Convert volume to massConvert volume to mass95 cm3•13.6 gcm3= 1.3 x 103g1.3 x 103g •1 lb454 g= 2.8 lb2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)
61. 61. Learning CheckLearning CheckOsmium is a very dense metal. What is itsOsmium is a very dense metal. What is itsdensity in g/cmdensity in g/cm33if 50.00 g of the metal occupiesif 50.00 g of the metal occupiesa volume of 2.22cma volume of 2.22cm33??1) 2.25 g/cm1) 2.25 g/cm332)2) 22.5 g/cm22.5 g/cm333)3) 111 g/cm111 g/cm33
62. 62. Solution2) Placing the mass and volume of the osmium metal2) Placing the mass and volume of the osmium metalinto the density setup, we obtaininto the density setup, we obtainD =D = massmass == 50.00 g50.00 g ==volumevolume2.22 cm2.22 cm33= 22.522522 g/cm= 22.522522 g/cm33= 22.5 g/cm= 22.5 g/cm33
63. 63. Volume DisplacementVolume DisplacementA solid displaces a matching volume of waterA solid displaces a matching volume of waterwhen the solid is placed in water.when the solid is placed in water.33 mL33 mL25 mL25 mL
64. 64. Learning CheckLearning CheckWhat is the density (g/cmWhat is the density (g/cm33) of 48 g of a metal if the) of 48 g of a metal if themetal raises the level of water in a graduatedmetal raises the level of water in a graduatedcylinder from 25 mL to 33 mL?cylinder from 25 mL to 33 mL?1) 0.2 g/ cm1) 0.2 g/ cm332) 6 g/m2) 6 g/m333) 252 g/cm3) 252 g/cm3333 mL33 mL25 mL25 mL
65. 65. Learning CheckLearning CheckWhich diagram represents the liquid layers in theWhich diagram represents the liquid layers in thecylinder?cylinder?(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91g/mL,) (W) water (1.0 g/mL)g/mL,) (W) water (1.0 g/mL)1)1) 2)2) 3)3)KKWWWVVVK
66. 66. Learning CheckLearning CheckThe density of octane, a component of gasoline, isThe density of octane, a component of gasoline, is0.702 g/mL. What is the mass, in kg, of 875 mL of0.702 g/mL. What is the mass, in kg, of 875 mL ofoctane?octane?1) 0.614 kg1) 0.614 kg2) 614 kg2) 614 kg3) 1.25 kg3) 1.25 kg
67. 67. Learning CheckLearning CheckIf blood has a density of 1.05 g/mL, howIf blood has a density of 1.05 g/mL, howmany liters of blood are donated if 575 g ofmany liters of blood are donated if 575 g ofblood are given?blood are given?1)1) 0.548 L0.548 L2)2) 1.25 L1.25 L3)3) 1.83 L1.83 L
68. 68. Learning CheckLearning CheckA group of students collected 125 empty aluminumA group of students collected 125 empty aluminumcans to take to the recycling center. If 21 cans makecans to take to the recycling center. If 21 cans make1.0 pound of aluminum, how many liters of1.0 pound of aluminum, how many liters ofaluminum (D=2.70 g/cmaluminum (D=2.70 g/cm33) are obtained from the) are obtained from thecans?cans?1) 1.0 L1) 1.0 L 2) 2.0 L2) 2.0 L 3) 4.0 L3) 4.0 L