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David measures a line to be
3.64cm long. If the actual measurement is
4cm, find David's relative error to the nearest hundredth.
Answer:

David measures a line to be $3.64 \mathrm{~cm}$ long. If the actual measurement is $4 \mathrm{~cm}$ , find David's relative error to the nearest hundredth. $\newline$ Answer:

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Full solution

Q. David measures a line to be

3.64 \mathrm{~cm}

long. If the actual measurement is

4 \mathrm{~cm}

, 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 value of the difference between the measured value and the actual value, divided by the actual value. It is often expressed as a percentage.
Calculate absolute error: Calculate the absolute error, which is the absolute difference between the measured value and the actual value. $\newline$ Absolute error = $|\text{Measured Value} - \text{Actual Value}|$ $\newline$ Absolute error = $|3.64 \text{ cm} - 4 \text{ cm}|$ $\newline$ Absolute error = $|-0.36 \text{ cm}|$ $\newline$ Absolute error = $0.36 \text{ cm}$
Calculate relative error: Calculate the relative error by dividing the absolute error by the actual value. $\newline$ Relative error = $\frac{\text{Absolute error}}{\text{Actual value}}$ $\newline$ Relative error = $\frac{0.36\,\text{cm}}{4\,\text{cm}}$ $\newline$ Relative error = $0.09$
Convert to percentage: Convert the relative error to a percentage by multiplying by $100$ and round to the nearest hundredth. $\newline$ Relative error percentage = Relative error $\times 100$ $\newline$ Relative error percentage = $0.09 \times 100$ $\newline$ Relative error percentage = $9\%$ $\newline$ To round to the nearest hundredth, we do not need to change anything since $9\%$ is already at the hundredth place when expressed as a decimal ( $0.09$ ).

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