Carter measures a line to be 8.75cm long. If the actual measurement is 9cm, find Carter's relative error to the nearest hundredth. 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. The absolute error is the difference between the measured value and the actual value. Absolute Error = |Measured Value - Actual Value| Absolute Error = |8.75 cm - 9 cm| Absolute Error = |-0.25 cm| Absolute Error = 0.25 cmCalculate relative error: Calculate the relative error. Relative Error = (Absolute Error / Actual Value) * 100 (to get a percentage) Relative Error = (0.25 cm / 9 cm) * 100 Relative Error = 0.027777... * 100 Relative Error = 2.7777...Round relative error: Round the relative error to the nearest hundredth. Relative Error ≈ 2.78%

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Carter measures a line to be
8.75cm long. If the actual measurement is
9cm, find Carter's relative error to the nearest hundredth.
Answer:

Carter measures a line to be $8.75 \mathrm{~cm}$ long. If the actual measurement is $9 \mathrm{~cm}$ , find Carter's relative error to the nearest hundredth. $\newline$ Answer:

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Q. Carter measures a line to be

8.75 \mathrm{~cm}

long. If the actual measurement is

9 \mathrm{~cm}

, find Carter'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. $\newline$ 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 = $|8.75 \text{ cm} - 9 \text{ cm}|$ $\newline$ Absolute Error = $|-0.25 \text{ cm}|$ $\newline$ Absolute Error = $0.25 \text{ cm}$
Calculate relative error: Calculate the relative error. $\newline$ Relative Error = $(\text{Absolute Error} / \text{Actual Value}) \times 100$ (to get a percentage) $\newline$ Relative Error = $(0.25 \, \text{cm} / 9 \, \text{cm}) \times 100$ $\newline$ Relative Error = $0.027777... \times 100$ $\newline$ Relative Error = $2.7777...$
Round relative error: Round the relative error to the nearest hundredth. $\newline$ Relative Error $\approx 2.78\%$