The actual dimensions of a rectangle are 8cm by 4cm. David measures the sides to be 8.37cm by 4.27cm. In calculating the area, what is the relative error, to the nearest hundredth. Answer:

Calculate Actual Area: Calculate the actual area of the rectangle using the actual dimensions. Actual area = length × width Actual area = 8 cm × 4 cm Actual area = 32 cm²Calculate Measured Area: Calculate the measured area of the rectangle using the measured dimensions. Measured area = measured length × measured width Measured area = 8.37 cm × 4.27 cm Measured area = 35.7399 cm²Calculate Absolute Error: Calculate the absolute error by subtracting the actual area from the measured area. Absolute error = |Measured area - Actual area| Absolute error = |35.7399 cm² - 32 cm²| Absolute error = 3.7399 cm²Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual area and then multiplying by 100 to get the percentage. Relative error = (Absolute error / Actual area) × 100% Relative error = (3.7399 cm² / 32 cm²) × 100% Relative error = 0.1168725 × 100% Relative error = 11.68725%Round Relative Error: Round the relative error to the nearest hundredth. Relative error (rounded) = 11.69%

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The actual dimensions of a rectangle are
8cm by
4cm. David measures the sides to be
8.37cm by
4.27cm. In calculating the area, what is the relative error, to the nearest hundredth.
Answer:

The actual dimensions of a rectangle are $8 \mathrm{~cm}$ by $4 \mathrm{~cm}$ . David measures the sides to be $8.37 \mathrm{~cm}$ by $4.27 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest hundredth. $\newline$ Answer:

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Q. The actual dimensions of a rectangle are

8 \mathrm{~cm}

4 \mathrm{~cm}

. David measures the sides to be

8.37 \mathrm{~cm}

4.27 \mathrm{~cm}

. In calculating the area, what is the relative error, to the nearest hundredth.

\newline

Answer:

Calculate Actual Area: Calculate the actual area of the rectangle using the actual dimensions. $\newline$ Actual area = $\text{length} \times \text{width}$ $\newline$ Actual area = $8\,\text{cm} \times 4\,\text{cm}$ $\newline$ Actual area = $32\,\text{cm}^2$
Calculate Measured Area: Calculate the measured area of the rectangle using the measured dimensions. $\newline$ Measured area = $\text{measured length} \times \text{measured width}$ $\newline$ Measured area = $8.37 \, \text{cm} \times 4.27 \, \text{cm}$ $\newline$ Measured area = $35.7399 \, \text{cm}^2$
Calculate Absolute Error: Calculate the absolute error by subtracting the actual area from the measured area. $\newline$ Absolute error = $|\text{Measured area} - \text{Actual area}|$ $\newline$ Absolute error = $|35.7399 \text{ cm}^2 - 32 \text{ cm}^2|$ $\newline$ Absolute error = $3.7399 \text{ cm}^2$
Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual area and then multiplying by $100$ to get the percentage. $\newline$ Relative error = $(\text{Absolute error} / \text{Actual area}) \times 100\%$ $\newline$ Relative error = $(3.7399 \, \text{cm}^2 / 32 \, \text{cm}^2) \times 100\%$ $\newline$ Relative error = $0.1168725 \times 100\%$ $\newline$ Relative error = $11$ . $68725$ \%
Round Relative Error: Round the relative error to the nearest hundredth. $\newline$ Relative error (rounded) = $11.69\%$