To find Carter's relative error, we can use the formula for relative error:
\[ \text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|} \]
In this case, the measured value is 9.3 cm and the actual value is 9 cm.
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Calculate the absolute error: \[ |\text{Measured Value} - \text{Actual Value}| = |9.3 - 9| = |0.3| = 0.3 \]
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Now, use the absolute error in the relative error formula: \[ \text{Relative Error} = \frac{0.3}{9} \]
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Perform the division: \[ \frac{0.3}{9} \approx 0.0333\ldots \]
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To express this relative error as a percentage, multiply by 100: \[ \text{Relative Error} \times 100 \approx 0.0333 \times 100 \approx 3.33% \]
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Finally, rounding to the nearest hundredth gives us: \[ \text{Relative Error} \approx 3.33% \]
Thus, Carter's relative error is approximately 3.33%.
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