Question
A student measures the length of a football field and reports it to be 294 feet long. The actual length of the field is 300 feet. What is the percentage error in the student's measurement?
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Answers
GPT-4o mini
To calculate the percentage error in the student's measurement, we can use the following formula:
\[
\text{Percentage Error} = \left( \frac{\text{Absolute Error}}{\text{True Value}} \right) \times 100
\]
The absolute error is the difference between the student's reported measurement and the actual length:
\[
\text{Absolute Error} = |\text{True Value} - \text{Measured Value}| = |300 - 294| = 6 \text{ feet}
\]
Now we can plug the values into the percentage error formula:
\[
\text{Percentage Error} = \left( \frac{6}{300} \right) \times 100
\]
Calculating that:
\[
\text{Percentage Error} = \left( 0.02 \right) \times 100 = 2\%
\]
Thus, the percentage error in the student's measurement is **2%**.
\[
\text{Percentage Error} = \left( \frac{\text{Absolute Error}}{\text{True Value}} \right) \times 100
\]
The absolute error is the difference between the student's reported measurement and the actual length:
\[
\text{Absolute Error} = |\text{True Value} - \text{Measured Value}| = |300 - 294| = 6 \text{ feet}
\]
Now we can plug the values into the percentage error formula:
\[
\text{Percentage Error} = \left( \frac{6}{300} \right) \times 100
\]
Calculating that:
\[
\text{Percentage Error} = \left( 0.02 \right) \times 100 = 2\%
\]
Thus, the percentage error in the student's measurement is **2%**.