Bob measures a line to be 7.7ft long. If the actual measurement is 8ft, find Bob'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 difference between the measured value and the actual value. Absolute error = |Measured Value - Actual Value| Absolute error = |7.7ft - 8ft| Absolute error = |-0.3ft| Absolute error = 0.3ftCalculate relative error: Calculate the relative error. Relative error = (Absolute Error / Actual Value) Relative error = (0.3ft / 8ft) Relative error = 0.0375Convert to nearest thousandth: Convert the relative error to the nearest thousandth. To express the relative error to the nearest thousandth, we round it to three decimal places. Relative error (to the nearest thousandth) = 0.038

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Grade 7

Percent error: word problems

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Q. Bob measures a line to be

7.7 \mathrm{ft}

long. If the actual measurement is

8 \mathrm{ft}

, find Bob'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 difference between the measured value and the actual value. $\newline$ Absolute error = $|\text{Measured Value} - \text{Actual Value}|$ $\newline$ Absolute error = $|7.7\text{ft} - 8\text{ft}|$ $\newline$ Absolute error = $|-0.3\text{ft}|$ $\newline$ Absolute error = $0.3\text{ft}$
Calculate relative error: Calculate the relative error. $\newline$ Relative error = $\frac{\text{Absolute Error}}{\text{Actual Value}}$ $\newline$ Relative error = $\frac{0.3\,\text{ft}}{8\,\text{ft}}$ $\newline$ Relative error = $0.0375$
Convert to nearest thousandth: Convert the relative error to the nearest thousandth. $\newline$ To express the relative error to the nearest thousandth, we round it to three decimal places. $\newline$ Relative error (to the nearest thousandth) = $0.038$