A measurement of length is recorded as 5.0 cm with an uncertainty of ±0.1 cm. Wh

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Question: A measurement of length is recorded as 5.0 cm with an uncertainty of ±0.1 cm. What is the relative error in this measurement?

Options:

Correct Answer: 0.01

Solution:

Relative error = (absolute error / measured value) = 0.1 / 5.0 = 0.02 or 2%.

A measurement of length is recorded as 5.0 cm with an uncertainty of ±0.1 cm. What is the relative error in this measurement?

A measurement of length is recorded as 5.0 cm with an uncertainty of ±0.1 cm. What is the relative error in this measurement?

Correct Answer: 2%

Step 1: Identify the absolute error, which is given as ±0.1 cm.
Step 2: Identify the measured value, which is 5.0 cm.
Step 3: Calculate the relative error using the formula: relative error = (absolute error / measured value).
Step 4: Substitute the values into the formula: relative error = 0.1 cm / 5.0 cm.
Step 5: Perform the division: 0.1 / 5.0 = 0.02.
Step 6: Convert the relative error to a percentage by multiplying by 100: 0.02 * 100 = 2%.

Relative Error – Relative error is a measure of the uncertainty of a measurement compared to the size of the measurement itself, expressed as a percentage.
Absolute Error – Absolute error is the difference between the measured value and the true value, which in this case is represented by the uncertainty.
Measurement Uncertainty – Measurement uncertainty indicates the range within which the true value is expected to lie, often expressed as ± a certain value.