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Question Video: Calculating an Absolute Error from a Relative Error Physics • 9th Grade

If the relative error in measuring an area of 320 m² was 0.03, calculate the absolute error for that measurement.

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Video Transcript

If the relative error in measuring an area of 320 meters squared was 0.03, calculate the absolute error for that measurement.

In this question, we’re asked to determine the absolute error of a measurement if we know the relative error. First, let’s remember that relative error is a way of showing the error proportional to the accepted value. We can recall that the equation for relative error is given by 𝑟 equals Δ𝑥 over 𝑥 zero, where 𝑟 is the relative error, Δ𝑥 is the absolute error, and 𝑥 zero is the accepted value.

Now let’s make the absolute error Δ𝑥 the subject. We can do this by multiplying both sides of the equation by the accepted value 𝑥 zero to give us Δ𝑥 equals 𝑟 multiplied by 𝑥 zero. We are told in the question that the relative error is equal to 0.03, which is a dimensionless number, so 𝑟 is equal to 0.03. The accepted value of the area is 320 meters squared. So 𝑥 zero is equal to 320 meters squared.

We can now substitute in the given values into the equation to find that the absolute error Δ𝑥 is equal to 0.03 multiplied by 320 meters squared. This gives us an answer of 9.6 meters squared, and this is the correct answer. The absolute error for this measurement is 9.6 meters squared.

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