1 Measurements. 2 Nature of Measurement Measurement - quantitative observation consisting of 2 parts...
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Transcript of 1 Measurements. 2 Nature of Measurement Measurement - quantitative observation consisting of 2 parts...
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Nature of MeasurementNature of MeasurementMeasurement - quantitative observation Measurement - quantitative observation
consisting of 2 partsconsisting of 2 parts
Part 1 - numberPart 1 - number Part 2 - scale (unit)Part 2 - scale (unit)
Examples:Examples:20 grams20 grams
6.63 6.63 Joule seconds Joule seconds
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International SystemInternational System(le Système International)(le Système International)
Based on metric system and units Based on metric system and units derived from metric system.derived from metric system.
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Dimensional AnalysisDimensional Analysisoror
The Unit Factor MethodThe Unit Factor Method
Proper use of “unit factors” leads to proper Proper use of “unit factors” leads to proper units in your answer. units in your answer.
Have X Wanted/Have = WantedHave X Wanted/Have = WantedWhere Wanted/Have = 1 or unityWhere Wanted/Have = 1 or unity
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Unit Factor PracticeUnit Factor Practice1. Convert 34.5 centimeters into inches (2.54cm/1 in).
2. Convert 2376 grams into kilograms.
3. Convert 14.02 Liters into gallons (3.785L/1.000 Gal).
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Uncertainty in MeasurementUncertainty in Measurement
A digit that must be A digit that must be estimatedestimated is is called called uncertainuncertain. A . A measurementmeasurement alwaysalways has some degree of has some degree of uncertainty in the last digit uncertainty in the last digit reported.reported.
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Precision and AccuracyPrecision and Accuracy
Accuracy Accuracy refers to the agreement of a refers to the agreement of a particular value with theparticular value with the true true value.value.
PrecisionPrecision refers to the degree of refers to the degree of agreement among several agreement among several measurements of the same quantity.measurements of the same quantity.
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Significant Figures - OverviewSignificant Figures - Overview
1.1. Nonzero integersNonzero integers
2.2. ZerosZeros
leading zerosleading zeros
captive zeroscaptive zeros
trailing zerostrailing zeros
3.3. Exact numbersExact numbers
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Significant Figures - DetailsSignificant Figures - Details
Nonzero integersNonzero integers always count always count as significant figures.as significant figures.
34563456
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Significant Figures - DetailsSignificant Figures - Details
ZerosZerosLeading zerosLeading zeros do not count as do not count as significant figures.significant figures.
0.04860.0486
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Significant Figures - DetailsSignificant Figures - Details
ZerosZeros Captive zerosCaptive zeros always count always count as as significant figures.significant figures.
16.0716.07
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Significant Figures - DetailsSignificant Figures - Details
ZerosZeros Trailing zerosTrailing zeros are significant are significant
only only if the number contains if the number contains a decimal point.a decimal point.
9.3009.300
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Significant Figures - DetailsSignificant Figures - Details
ZerosZeros Trailing zerosTrailing zeros are significant are significant
only only if the number contains if the number contains a decimal point.a decimal point.
93009300
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Significant Figures - DetailsSignificant Figures - Details
ZerosZeros 93009300 could be 2, could could be 2, could
be 3, could be 4???be 3, could be 4???It is ambiguous.It is ambiguous.Therefore, Change it to Therefore, Change it to
Scientific NotationScientific Notation
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Significant Figures - DetailsSignificant Figures - Details
ZerosZeros 930093002 sig figs 9.3 X 102 sig figs 9.3 X 1033
3 sig figs 9.30 X 103 sig figs 9.30 X 1033
4 sig figs 9.300 X 104 sig figs 9.300 X 1033
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Significant Figures - DetailsSignificant Figures - Details
• Exact numbersExact numbers have an have an infinite number of significant infinite number of significant figures.figures.
11 inch = inch = 2.54 2.54 cm exactlycm exactly
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Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations
Multiplication and Division: Multiplication and Division: # sig figs in the result equals the # sig figs in the result equals the number in the least precise number in the least precise measurement used in the measurement used in the calculation.calculation.
6.38 6.38 2.0 = 2.0 =
12.76 12.76
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Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations
Addition and Subtraction: Addition and Subtraction: # sig figs in # sig figs in the result equals the number of the result equals the number of decimal places in the least precise decimal places in the least precise measurement.measurement.
6.8 + 11.934 =6.8 + 11.934 =
18.734 18.734 __________________________
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TemperatureTemperature
Celsius scale =Celsius scale =CCKelvin scale = KKelvin scale = K
Fahrenheit scale =Fahrenheit scale =FF
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Temperature ScalesTemperature Scales• Fahrenheit Scale, °F
– Water’s freezing point = 32°F, boiling point = 212°F
• Celsius Scale, °C– Temperature unit larger than the Fahrenheit– Water’s freezing point = 0°C, boiling point = 100°C
• Kelvin Scale, K– Temperature unit same size as Celsius– Water’s freezing point = 273 K, boiling point = 373
K