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, 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.

2 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, 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.

3 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,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.

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,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)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)

5 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)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)

6 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)

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 UncertaintiesDivision with Multiple UncertaintiesWhat if both numbers have uncertainties?Terry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesDivision with Multiple UncertaintiesWhat if both numbers have uncertainties?Terry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesDivision with Multiple Uncertainties - ExampleDivision operates just like the rules for multiplication, (xy) (xy)( xx+ yy)If we want to find the Uncertainty inx/y, we can just make anew quantity,w, wherew= 1/y, so thatx/y=xw, so we know that (xw) (xw)( xx+ ww)

9 Terry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesDivision with Multiple Uncertainties - ExampleDivision operates just like the rules for multiplication, (xy) (xy)( xx+ yy)If we want to find the Uncertainty inx/y, we can just make anew quantity,w, wherew= 1/y, so thatx/y=xw, so we know that (xw) (xw)( xx+ ww)Terry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesDivision with Multiple Uncertainties - ExampleDivision operates just like the rules for multiplication, (xy) (xy)( xx+ yy)If we want to find the Uncertainty inx/y, we can just make anew quantity,w, wherew= 1/y, so thatx/y=xw, so we know that (xw) (xw)( xx+ ww)

10 Terry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesDivision with Multiple Uncertainties - ExampleDivision operates just like the rules for multiplication, (xy) (xy)( xx+ yy)If we want to find the Uncertainty inx/y, we can just make anew quantity,w, wherew= 1/y, so thatx/y=xw, so we know that (xw) (xw)( xx+ ww)Terry SturtevantUncertainty Calculations - Division Wilfrid Laurier UniversityCalculations with UncertaintiesRecapInversionDivision with Multiple UncertaintiesDivision with Multiple Uncertainties - ExampleDivision operates just like the rules for multiplication, (xy) (xy)( xx+ yy)If we want to find the Uncertainty inx/y, we can just make anew quantity,w, wherew= 1/y, so thatx/y=xw, so we know that (xw) (xw)( xx+ ww)