Calculate 73.936 with Absolute Uncertainty

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SUMMARY

The discussion focuses on calculating the value of 73.936 with an absolute uncertainty of ±0.19% in the context of a complex mathematical expression involving both addition and division. The equation presented is 73.936(+ 0.19%) divided by the sum of two uncertainties: (0.00455 + 0.00096) and (0.011889(+0.73%)). Participants clarify that absolute uncertainty should be calculated first for the addition, followed by applying the appropriate rules for division. The confusion arises around whether to use absolute or relative uncertainty during the division, with a consensus that absolute uncertainty is necessary for the initial calculation.

PREREQUISITES
  • Understanding of absolute and relative uncertainty calculations
  • Familiarity with scientific notation
  • Knowledge of basic arithmetic operations involving uncertainties
  • Experience with mathematical expressions involving addition and division
NEXT STEPS
  • Study the principles of absolute and relative uncertainty in detail
  • Learn how to express results in scientific notation
  • Explore examples of uncertainty calculations in complex equations
  • Review the rules for combining uncertainties in addition and division
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Homework Statement


Perform the calculation and report answer in proper scientific notation with absolute uncertainty

73.936(+ 0.19%) / [(0.00455+ 0.00096) + (0.011889(+0.73%))]

Homework Equations



Addition/Subtraction:
Absolute uncertainty = square root(uncertainty1 + uncertainty2)
Relative uncertainty = Absolute uncertainty divided by answer to addition(or subtraction)

Multiplication/Division:
Relative uncertainty = (uncertainty divided by corresponding value)2

The Attempt at a Solution



How would I do the absolute uncertainty since there is both subtraction and division?
 
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Do the addition first and determine the uncertainty for the part solution. Then, using that uncertainty, divide and use the proper rule to determine the uncertainty in the result.
 


But after I find the uncertainty for the addition,it is going to be the absolute uncertainty.Would I use the absolute uncertainty when calculating the division part? Or would I have to calculate the relative uncertainty for the addition part and use that for the division part? The thing that is confusing me is which uncertainty to use for the division part, the relative or absolute uncertainty from the addition part.
Would I use the absolute uncertainty because when finding the uncertainty through division, the absolute uncertainty calculation always comes first before the relative uncertainty
Thanks
 

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