A measurement of 30 m has an error of ±0.1 m. What is the true value if the meas

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Question: A measurement of 30 m has an error of ±0.1 m. What is the true value if the measurement is taken as the average?

Options:

Correct Answer: 30.05 m

Solution:

True value is taken as the average of the measured value and the error, which is (30 + 29.9) / 2 = 30.05 m.

A measurement of 30 m has an error of ±0.1 m. What is the true value if the measurement is taken as the average?

A measurement of 30 m has an error of ±0.1 m. What is the true value if the measurement is taken as the average?

Step 1: Identify the measured value, which is 30 m.
Step 2: Identify the error, which is ±0.1 m.
Step 3: Calculate the lower limit of the measurement by subtracting the error from the measured value: 30 m - 0.1 m = 29.9 m.
Step 4: Calculate the upper limit of the measurement by adding the error to the measured value: 30 m + 0.1 m = 30.1 m.
Step 5: Now you have two values: 29.9 m (lower limit) and 30.1 m (upper limit).
Step 6: To find the true value, take the average of the lower and upper limits: (29.9 m + 30.1 m) / 2.
Step 7: Calculate the average: (29.9 + 30.1) / 2 = 30.0 m.
Step 8: The true value is 30.0 m.

Measurement and Error Analysis – Understanding how to interpret measurements with associated errors and calculating true values.
Averaging Values – The process of finding the average of two or more values, particularly in the context of measurements and their uncertainties.