To find David's relative error, we first need to calculate the absolute error and then use it to find the relative error.
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Calculate the absolute error: \[ \text{Absolute Error} = |\text{Measured Value} - \text{Actual Value}| \] Given that David measured 5.25 inches and the actual measurement is 5 inches, we have: \[ \text{Absolute Error} = |5.25 - 5| = |0.25| = 0.25 \text{ inches} \]
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Calculate the relative error: \[ \text{Relative Error} = \frac{\text{Absolute Error}}{\text{Actual Value}} \] Using the absolute error we calculated and the actual value (5 inches): \[ \text{Relative Error} = \frac{0.25}{5} \]
Performing the division: \[ \text{Relative Error} = 0.05 \]
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Convert the relative error to a percentage (if needed): To express the relative error as a percentage, we multiply by 100: \[ \text{Relative Error (percentage)} = 0.05 \times 100 = 5% \]
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Final Representation as a Decimal: Since you asked for the relative error to the nearest thousandth as a decimal, we write: \[ \text{Relative Error} = 0.050 \]
Thus, David's relative error, to the nearest thousandth, is 0.050.
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