Eric measures a line to be 9.38ft long. If the actual measurement is 9ft, find Eric's relative error to the nearest thousandth. Answer:

Calculate Absolute Error: To find the relative error, we need to calculate the absolute error and then divide it by the true value. The absolute error is the difference between the measured value and the true value. Absolute error = |Measured Value - True Value|Find Absolute Error: Now we calculate the absolute error using the values given. Absolute error = |9.38ft - 9ft| = |0.38ft|Calculate Relative Error: The absolute error is 0.38ft. Now we need to find the relative error by dividing the absolute error by the true value. Relative error = Absolute error / True ValueFind Relative Error: We calculate the relative error using the absolute error we found and the true value. Relative error = 0.38ft / 9ftRound Relative Error: Performing the division to find the relative error. Relative error = 0.042222...We need to round the relative error to the nearest thousandth as asked in the question prompt. Relative error (rounded) = 0.042

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Eric measures a line to be
9.38ft long. If the actual measurement is
9ft, find Eric's relative error to the nearest thousandth.
Answer:

Eric measures a line to be $9.38 \mathrm{ft}$ long. If the actual measurement is $9 \mathrm{ft}$ , find Eric's relative error to the nearest thousandth. $\newline$ Answer:

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Q. Eric measures a line to be

9.38 \mathrm{ft}

long. If the actual measurement is

9 \mathrm{ft}

, find Eric's relative error to the nearest thousandth.

\newline

Answer:

Calculate Absolute Error: To find the relative error, we need to calculate the absolute error and then divide it by the true value. The absolute error is the difference between the measured value and the true value. $\newline$ Absolute error = $\lvert\text{Measured Value} - \text{True Value}\rvert$
Find Absolute Error: Now we calculate the absolute error using the values given. $\newline$ Absolute error = $|9.38\,\text{ft} - 9\,\text{ft}| = |0.38\,\text{ft}|$
Calculate Relative Error: The absolute error is $0.38\text{ft}$ . Now we need to find the relative error by dividing the absolute error by the true value. $\newline$ Relative error = \frac{\text{Absolute error}}{\text{True Value}}
Find Relative Error: We calculate the relative error using the absolute error we found and the true value. $\newline$ Relative error = $\frac{0.38\text{ft}}{9\text{ft}}$
Round Relative Error: Performing the division to find the relative error. $\text{Relative error} = 0.042222\ldots$
Round Relative Error: Performing the division to find the relative error. Relative error = $0.042222\ldots$ We need to round the relative error to the nearest thousandth as asked in the question prompt. Relative error (rounded) = $0.042$