Uncertainty Calculations (Division) - Wilfrid Laurier ...

1 Calculations with UncertaintiesRecapUncertainty Calculations - DivisionWilfrid Laurier UniversityTerry SturtevantWilfrid Laurier UniversityMay 9, 2013 Terry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesCalculations with uncertaintiesWhen quantities with uncertainties are combined, the resultshave uncertainties as is a discussion the following examples, the values ofx= 2 1 andy= will be SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesCalculations with uncertaintiesWhen quantities with uncertainties are combined, the resultshave uncertainties as is a discussion the following examples.

2 The values ofx= 2 1 andy= will be SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesCalculations with uncertaintiesWhen quantities with uncertainties are combined, the resultshave uncertainties as is a discussion the following examples, the values ofx= 2 1 andy= will be SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesCalculations with uncertaintiesWhen quantities with uncertainties are combined, the resultshave uncertainties as is a discussion the following examples.

3 The values ofx= 2 1 andy= will be SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversionInversion with uncertaintiesTerry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversionInversion with uncertaintiesTerry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversion - ExampleIf we take the inverse of one of these numbers,z=1y= zcan be + be asbigas zcan be be assmallas SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversion - ExampleIf we take the inverse of one of these numbers.

4 Z=1y= zcan be + be asbigas zcan be be assmallas SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversion - ExampleIf we take the inverse of one of these numbers,z=1y= zcan be + be asbigas zcan be be assmallas SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversion - ExampleIf we take the inverse of one of these numbers.

5 Z=1y= zcan be + be asbigas zcan be be assmallas SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversion - ExampleIf we take the inverse of one of these numbers,z=1y= zcan be + be asbigas zcan be be assmallas SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversion - ExampleIf we take the inverse of one of these numbers.

6 Z=1y= zcan be + be asbigas zcan be be assmallas SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesInversion - ExampleIf we take the inverse of one of these numbers,z=1y= zcan be + be asbigas zcan be be assmallas SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)

7 The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)

8 The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)

9 The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)

10 The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesTo summarize,zcan be + ofzisz= we can sayz we see that z =( ) =( yy)1ySo in general, 1y=1y( yy)The proportional Uncertainty in the inverse of a numberis the same as the proportional Uncertainty in SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesDivision with Multiple UncertaintiesWhat if both numbers have uncertainties?