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David measures a line to be 10.08 in long. If the actual measurement is
10in, find David's relative error to the nearest hundredth.
Answer:

David measures a line to be $10$ . $08$ in long. If the actual measurement is $10 \mathrm{in}$ , find David's relative error to the nearest hundredth. $\newline$ Answer:

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Full solution

Q. David measures a line to be

10

.

08

in long. If the actual measurement is

10 \mathrm{in}

, find David's relative error to the nearest hundredth.

\newline

Answer:

Understand relative error: Understand the concept of relative error. Relative error is the absolute error divided by the actual measurement, often expressed as a percentage. The absolute error is the difference between the measured value and the actual value.
Calculate absolute error: Calculate the absolute error. $\newline$ Absolute error = $|\text{Measured Value} - \text{Actual Value}|$ $\newline$ Absolute error = $|10.08 \text{ in} - 10 \text{ in}|$ $\newline$ Absolute error = $|0.08 \text{ in}|$ $\newline$ Absolute error = $0.08 \text{ in}$
Calculate relative error: Calculate the relative error. $\newline$ Relative error = $(\text{Absolute error} / \text{Actual Value}) \times 100$ (to get the percentage) $\newline$ Relative error = $(0.08 \, \text{in} / 10 \, \text{in}) \times 100$ $\newline$ Relative error = $0.008 \times 100$ $\newline$ Relative error = $0.8\%$
Round relative error: Round the relative error to the nearest hundredth. $\newline$ Since the relative error is already at the hundredth place as $0.8\%$ , we do not need to round it further.

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