If the area of a rectangle is calculated as 30 m² with an uncertainty of ±0.5 m²

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Question: If the area of a rectangle is calculated as 30 m² with an uncertainty of ±0.5 m², what is the relative error in the area measurement?

Options:

Correct Answer: 0.0167

Solution:

Relative error = (absolute error / measured value) = 0.5 / 30 = 0.0167.

If the area of a rectangle is calculated as 30 m² with an uncertainty of ±0.5 m², what is the relative error in the area measurement?

If the area of a rectangle is calculated as 30 m² with an uncertainty of ±0.5 m², what is the relative error in the area measurement?

Step 1: Identify the measured value of the area of the rectangle, which is 30 m².
Step 2: Identify the absolute error, which is the uncertainty in the measurement, given as ±0.5 m².
Step 3: Use the formula for relative error, which is: relative error = (absolute error / measured value).
Step 4: Substitute the values into the formula: relative error = 0.5 m² / 30 m².
Step 5: Calculate the relative error: 0.5 / 30 = 0.0167.
Step 6: The relative error can also be expressed as a percentage by multiplying by 100, which gives 1.67%.

Area Measurement – Understanding how to calculate the area of a rectangle and the implications of uncertainty in measurements.
Relative Error – Calculating the relative error as the ratio of absolute error to the measured value.
Uncertainty in Measurements – Recognizing how uncertainty affects the precision of calculated values.