To calculate Carter's relative error, we use the formula for relative error:
\[ \text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{\text{Actual Value}} \]
Where:
- Measured Value = 5.8 cm
- Actual Value = 6 cm
First, we find the absolute error:
\[ |\text{Measured Value} - \text{Actual Value}| = |5.8 - 6| = | -0.2 | = 0.2 \]
Next, we substitute this into the formula for relative error:
\[ \text{Relative Error} = \frac{0.2}{6} \]
Calculating this gives:
\[ \text{Relative Error} = \frac{0.2}{6} \approx 0.0333\ldots \]
To express this as a percentage, we multiply by 100:
\[ \text{Relative Error as Percentage} \approx 0.0333 \times 100 \approx 3.33% \]
Finally, rounding to the nearest hundredth, we find:
\[ \text{Relative Error} \approx 0.03 \text{ (as a decimal)}, \quad \text{or} \quad 3.33% \text{ (as a percentage)} \]
Thus, Carter's relative error is approximately 0.03 (or 3.33%).
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