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What happens to the percentage uncertainty if you raise the measurement to a power?

a) It increases
b) It decreases
c) It remains the same
d) It becomes zero

User Mobilecat
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1 Answer

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Final answer:

The percentage uncertainty of a measurement increases when the measurement is raised to a power. This is because the percentage uncertainty is multiplied by the power, indicating a direct relation between the power and the uncertainty increase.

Step-by-step explanation:

When a measurement is raised to a power, the percentage uncertainty of the measurement generally follows a rule that it is multiplied by the power to which the measurement is raised. For instance, if a value A with a percentage uncertainty of 5% (0.05) is squared (A^2), the percentage uncertainty of the resulting value becomes 2 × 5% = 10%. If the value is cubed (A^3), the percentage uncertainty would be 3 × 5% = 15%, and so on. Therefore, the correct answer to the given question is a) It increases. The percentage uncertainty is a measure of the reliability of a measurement and is tied directly to the precision of the measuring device. The precision refers to how closely repeated measurements agree with each other, while accuracy refers to how close a measurement is to the true value. A decrease in either precision or accuracy can result in a higher uncertainty, but it is the precision that is directly related to the capture of uncertainty in measurements, especially when considering raising to a power.

User Brooklynsweb
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