To find Bob's relative error, we first need to calculate the error in his measurement and then express this error relative to the actual measurement.
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Calculate the error: \[ \text{Error} = \text{Measured value} - \text{Actual value} = 9.28 \text{ ft} - 9 \text{ ft} = 0.28 \text{ ft} \]
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Calculate the relative error: Relative error is given by the formula: \[ \text{Relative Error} = \frac{\text{Error}}{\text{Actual value}} \] Substituting the values we have: \[ \text{Relative Error} = \frac{0.28 \text{ ft}}{9 \text{ ft}} \approx 0.0311111111 \]
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Convert to a percentage: To express the relative error as a percentage, we multiply by 100: \[ \text{Relative Error (percent)} = 0.0311111111 \times 100 \approx 3.11111111% \]
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Round to the nearest thousandth: We round \(3.11111111%\) to the nearest thousandth: \[ \text{Rounded Relative Error} \approx 3.111% \]
So, Bob's relative error, to the nearest thousandth, is approximately 3.111%.