Alex measures a line to be 6.62ft long. If the actual measurement is 7ft, find Alex's relative error to the nearest thousandth. Answer:

Understand relative error: Understand the concept of relative error. Relative error is the absolute value of the difference between the measured value and the actual value, divided by the actual value. It is often expressed as a percentage or a decimal.Calculate absolute error: Calculate the absolute error. The absolute error is the absolute value of the difference between the measured value and the actual value. Absolute error = |Measured Value - Actual Value| Absolute error = |6.62ft - 7ft| Absolute error = |-0.38ft| Absolute error = 0.38ftCalculate relative error: Calculate the relative error. Relative error = (Absolute error / Actual Value) Relative error = (0.38ft / 7ft) Relative error ≈ 0.0542857Convert to nearest thousandth: Convert the relative error to the nearest thousandth. To convert to the nearest thousandth, we round the relative error to three decimal places. Relative error ≈ 0.054

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Grade 7

Percent error: word problems

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Q. Alex measures a line to be

6.62 \mathrm{ft}

long. If the actual measurement is

7 \mathrm{ft}

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

\newline

Answer:

Understand relative error: Understand the concept of relative error. Relative error is the absolute value of the difference between the measured value and the actual value, divided by the actual value. It is often expressed as a percentage or a decimal.
Calculate absolute error: Calculate the absolute error. $\newline$ The absolute error is the absolute value of the difference between the measured value and the actual value. $\newline$ Absolute error = $|\text{Measured Value} - \text{Actual Value}|$ $\newline$ Absolute error = $|6.62\text{ft} - 7\text{ft}|$ $\newline$ Absolute error = $|-0.38\text{ft}|$ $\newline$ Absolute error = $0.38\text{ft}$
Calculate relative error: Calculate the relative error. $\newline$ Relative error = $\frac{\text{Absolute error}}{\text{Actual Value}}$ $\newline$ Relative error = $\frac{0.38\,\text{ft}}{7\,\text{ft}}$ $\newline$ Relative error \approx $0$ . $0542857$
Convert to nearest thousandth: Convert the relative error to the nearest thousandth. $\newline$ To convert to the nearest thousandth, we round the relative error to three decimal places. $\newline$ Relative error $\approx 0.054$