The actual dimensions of a rectangle are 10cm by 9cm. Carter measures the sides to be 9.9cm by 8.97cm. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Calculate actual area: Calculate the actual area of the rectangle. The formula for the area of a rectangle is length × width. Actual area = 10 cm × 9 cm.Perform actual area calculation: Perform the calculation for the actual area. Actual area = 10 cm × 9 cm = 90 cm².Calculate measured area: Calculate the measured area of the rectangle. Measured area = 9.9 cm × 8.97 cm.Perform measured area calculation: Perform the calculation for the measured area. Measured area = 9.9 cm × 8.97 cm = 88.803 cm².Calculate absolute error: Calculate the absolute error in the area. Absolute error = |Actual area - Measured area|.Perform absolute error calculation: Perform the calculation for the absolute error. Absolute error = |90 cm² - 88.803 cm²| = 1.197 cm².Calculate relative error: Calculate the relative error. Relative error = Absolute error / Actual area.Perform relative error calculation: Perform the calculation for the relative error. Relative error = 1.197 cm² / 90 cm².Evaluate relative error: Evaluate the relative error to the nearest thousandth. Relative error ≈ 0.0133 (rounded to the nearest thousandth).

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The actual dimensions of a rectangle are
10cm by
9cm. Carter measures the sides to be
9.9cm by
8.97cm. In calculating the area, what is the relative error, to the nearest thousandth.
Answer:

The actual dimensions of a rectangle are $10 \mathrm{~cm}$ by $9 \mathrm{~cm}$ . Carter measures the sides to be $9.9 \mathrm{~cm}$ by $8.97 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer:

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Q. The actual dimensions of a rectangle are

10 \mathrm{~cm}

9 \mathrm{~cm}

. Carter measures the sides to be

9.9 \mathrm{~cm}

8.97 \mathrm{~cm}

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

\newline

Answer:

Calculate actual area: Calculate the actual area of the rectangle. $\newline$ The formula for the area of a rectangle is $\text{length} \times \text{width}$ . $\newline$ Actual area = $10 \, \text{cm} \times 9 \, \text{cm}$ .
Perform actual area calculation: Perform the calculation for the actual area. $\newline$ Actual area = $10\,\text{cm} \times 9\,\text{cm} = 90\,\text{cm}^2$ .
Calculate measured area: Calculate the measured area of the rectangle. $\newline$ Measured area = $9.9\,\text{cm} \times 8.97\,\text{cm}$ .
Perform measured area calculation: Perform the calculation for the measured area. $\newline$ Measured area = $9.9\,\text{cm} \times 8.97\,\text{cm} = 88.803\,\text{cm}^2$ .
Calculate absolute error: Calculate the absolute error in the area. $\newline$ Absolute error = $|\text{Actual area} - \text{Measured area}|$ .
Perform absolute error calculation: Perform the calculation for the absolute error. $\newline$ Absolute error = $|90 \, \text{cm}^2 - 88.803 \, \text{cm}^2| = 1.197 \, \text{cm}^2$ .
Calculate relative error: Calculate the relative error. $\newline$ Relative error = $\frac{\text{Absolute error}}{\text{Actual area}}$ .
Perform relative error calculation: Perform the calculation for the relative error. Relative error = $\frac{1.197 \, \text{cm}^2}{90 \, \text{cm}^2}.$
Evaluate relative error: Evaluate the relative error to the nearest thousandth. $\newline$ Relative error $\approx 0.0133$ (rounded to the nearest thousandth).