1 measurements. 2 nature of measurement measurement - quantitative observation consisting of 2 parts...

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MeasurementsMeasurements

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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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The Fundamental SI UnitsThe Fundamental SI Units

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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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ZerosZerosLeading zerosLeading zeros do not count as do not count as significant figures.significant figures.

0.04860.0486

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ZerosZeros Captive zerosCaptive zeros always count always count as as significant figures.significant figures.

16.0716.07

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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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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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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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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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• 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

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TemperatureTemperature

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Type Unit ConversionsType Unit ConversionsWhat if I want to convert a mass unit into a volume unit? For example, can I convert grams into milliliters?

g X --------- = mL

g X ml/g = mL

grams/milliliter is density

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