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Questions and Answers
What is the range of true values for a measurement reported as 2.45 cm +/- 0.01 cm?
What is the range of true values for a measurement reported as 2.45 cm +/- 0.01 cm?
How is relative uncertainty defined?
How is relative uncertainty defined?
What happens to absolute uncertainties when adding measurements?
What happens to absolute uncertainties when adding measurements?
What should be done with percentage uncertainties when multiplying measurements?
What should be done with percentage uncertainties when multiplying measurements?
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When dealing with a formula that has an exponent, how is uncertainty treated?
When dealing with a formula that has an exponent, how is uncertainty treated?
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What does dimensional analysis help check for in a relationship?
What does dimensional analysis help check for in a relationship?
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Which of the following symbols represents mass in dimensional analysis?
Which of the following symbols represents mass in dimensional analysis?
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What are the dimensions of density?
What are the dimensions of density?
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Study Notes
Errors/Uncertainties
- Absolute uncertainty is a number added to a reported value, defining the range of true values. For example, 2.45cm ± 0.01 cm means the true value is between 2.44 cm and 2.46 cm.
- Absolute uncertainty depends on the measuring instrument.
- Absolute Uncertainty = (Smallest graduation / 2) x Number of ends
Relative Uncertainty
- Relative uncertainty is the ratio of absolute uncertainty to the reported value.
- Relative Uncertainty = (Absolute Uncertainty / Reported Value)
- For example, if a length is 2.45 cm ± 0.01 cm, the relative uncertainty is 0.01 cm / 2.45 cm = 0.0041.
- Relative uncertainty is unitless.
Percentage Uncertainty
- Percentage uncertainty is the product of the relative uncertainty and 100%.
- % Uncertainty = (Relative Uncertainty) x 100%
Rules for Operating with Errors/Uncertainties
- Addition/Subtraction: Add the absolute uncertainties.
- Multiplication/Division: Add the relative (or percentage) uncertainties.
- Exponents: Multiply the percentage uncertainty of the base measurement by the exponent.
Dimensional Analysis
- Dimensions refer to the base quantities (like length, mass, and time) that make up a physical quantity.
- Dimensional analysis is used to check if a relationship is correct by ensuring the dimensions on both sides of an equation are the same. This is called homogeneity.
- Units for base quantities are:
- Length: [L]
- Mass: [M]
- Time: [T]
- Example: Density's dimensions = [M]/[L³] (derived from mass/volume dimensions)
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Description
This quiz explores the concepts of absolute, relative, and percentage uncertainties in measurement. It covers how to calculate these uncertainties and the rules for operating with them in various mathematical operations. Test your understanding of how uncertainties impact reported values in scientific measurements.
