The actual dimensions of a rectangle are 10cm by 6cm. David measures the sides to be 9.68cm by 6.04cm. 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. The formula for the area of a rectangle is length × width. Actual area = 10cm × 6cm = 60cm².Calculate Measured Area: Calculate the measured area of the rectangle using the measured dimensions. Measured area = 9.68cm × 6.04cm. Let's perform the multiplication to find the measured area. Measured area = 58.4512cm².Calculate Absolute Error: Calculate the absolute error by subtracting the actual area from the measured area. Absolute error = |Measured area - Actual area|. Absolute error = |58.4512cm² - 60cm²|. Absolute error = |-1.5488cm²|. Since we are looking for the absolute value, we take the positive value of the result. Absolute error = 1.5488cm².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. Relative error = (Absolute error / Actual area) × 100. Relative error = (1.5488cm² / 60cm²) × 100. Let's perform the division and multiplication to find the relative error. Relative error = (0.02581333...) × 100. Relative error = 2.581333...%.Round Relative Error: Round the relative error to the nearest hundredth. Relative error ≈ 2.58%.

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The actual dimensions of a rectangle are
10cm by
6cm. David measures the sides to be
9.68cm by
6.04cm. In calculating the area, what is the relative error, to the nearest hundredth.
Answer:

The actual dimensions of a rectangle are $10 \mathrm{~cm}$ by $6 \mathrm{~cm}$ . David measures the sides to be $9.68 \mathrm{~cm}$ by $6.04 \mathrm{~cm}$ . 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

10 \mathrm{~cm}

6 \mathrm{~cm}

. David measures the sides to be

9.68 \mathrm{~cm}

6.04 \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. $\newline$ The formula for the area of a rectangle is $\text{length} \times \text{width}$ . $\newline$ Actual area = $10\,\text{cm} \times 6\,\text{cm} = 60\,\text{cm}^2$ .
Calculate Measured Area: Calculate the measured area of the rectangle using the measured dimensions. $\newline$ Measured area = $9.68\,\text{cm} \times 6.04\,\text{cm}$ . $\newline$ Let's perform the multiplication to find the measured area. $\newline$ Measured area = $58.4512\,\text{cm}^2$ .
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 = $|58.4512\,\text{cm}^2 - 60\,\text{cm}^2|$ . $\newline$ Absolute error = $|-1.5488\,\text{cm}^2|$ . $\newline$ Since we are looking for the absolute value, we take the positive value of the result. $\newline$ Absolute error = $1.5488\,\text{cm}^2$ .
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. $\text{Relative error} = \frac{\text{Absolute error}}{\text{Actual area}} \times 100$ . $\text{Relative error} = \frac{1.5488\,\text{cm}^2}{60\,\text{cm}^2} \times 100$ .Let's perform the division and multiplication to find the relative error. $\text{Relative error} = (0.02581333\ldots) \times 100$ . $\text{Relative error} = 2.581333\ldots\%$ .
Round Relative Error: Round the relative error to the nearest hundredth. $\newline$ Relative error $\approx 2.58\%$ .