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Eric measures a line to be 2.92 in long. If the actual measurement is 3 in, find Eric's relative error to the nearest hundredth.
Answer:

Eric measures a line to be $2$ . $92$ in long. If the actual measurement is $3$ in, find Eric's relative error to the nearest hundredth. $\newline$ Answer:

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Full solution

Q. Eric measures a line to be

2

.

92

in long. If the actual measurement is

3

in, find Eric'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 = $|2.92 \text{ in} - 3 \text{ in}|$ $\newline$ Absolute error = $|-0.08 \text{ in}|$ (Taking the absolute value) $\newline$ Absolute error = $0.08 \text{ in}$
Calculate relative error: Calculate the relative error. $\newline$ Relative error = $\frac{\text{Absolute error}}{\text{Actual Value}}$ $\newline$ Relative error = $\frac{0.08 \, \text{in}}{3 \, \text{in}}$ $\newline$ Relative error = $0.026666\ldots$
Round relative error: Round the relative error to the nearest hundredth. $\newline$ Relative error (to the nearest hundredth) = $0.03$

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