The actual dimensions of a rectangle are 10ft by 10ft. Alex measures the sides to be 9.85ft by 9.59ft. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Calculate Actual Area: To find the relative error, we first need to calculate the actual area of the rectangle and the measured area of the rectangle. The formula for the area of a rectangle is length × width.Calculate Measured Area: Calculate the actual area using the actual dimensions: 10ft × 10ft = 100ft².Find Absolute Error: Calculate the measured area using the measured dimensions: 9.85ft × 9.59ft.Calculate Relative Error: Perform the multiplication to find the measured area: 9.85ft × 9.59ft = 94.3915ft².Round Relative Error: Now, we need to find the absolute error, which is the difference between the actual area and the measured area. Absolute error = |Actual Area - Measured Area|.Calculate the absolute error: |100ft² - 94.3915ft²| = 5.6085ft².To find the relative error, we divide the absolute error by the actual area. Relative error = Absolute error / Actual Area.Perform the division to find the relative error: 5.6085ft² / 100ft² = 0.056085.Finally, we round the relative error to the nearest thousandth: 0.056085 rounded to the nearest thousandth is 0.056.

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The actual dimensions of a rectangle are
10ft by
10ft. Alex measures the sides to be
9.85ft by
9.59ft. In calculating the area, what is the relative error, to the nearest thousandth.
Answer:

The actual dimensions of a rectangle are $10 \mathrm{ft}$ by $10 \mathrm{ft}$ . Alex measures the sides to be $9.85 \mathrm{ft}$ by $9.59 \mathrm{ft}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer:

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Grade 7

Percent error: word problems

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Q. The actual dimensions of a rectangle are

10 \mathrm{ft}

10 \mathrm{ft}

. Alex measures the sides to be

9.85 \mathrm{ft}

9.59 \mathrm{ft}

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

\newline

Answer:

Calculate Actual Area: To find the relative error, we first need to calculate the actual area of the rectangle and the measured area of the rectangle. The formula for the area of a rectangle is $length \times width$ .
Calculate Measured Area: Calculate the actual area using the actual dimensions: $10\text{ft} \times 10\text{ft} = 100\text{ft}^2$ .
Find Absolute Error: Calculate the measured area using the measured dimensions: $9.85\,\text{ft} \times 9.59\,\text{ft}.$
Calculate Relative Error: Perform the multiplication to find the measured area: $9.85\,\text{ft} \times 9.59\,\text{ft} = 94.3915\,\text{ft}^2$ .
Round Relative Error: Now, we need to find the absolute error, which is the difference between the actual area and the measured area. Absolute error = $|\text{Actual Area} - \text{Measured Area}|$ .
Round Relative Error: Now, we need to find the absolute error, which is the difference between the actual area and the measured area. Absolute error = $|\text{Actual Area} - \text{Measured Area}|$ .Calculate the absolute error: $|100\text{ft}^2 - 94.3915\text{ft}^2| = 5.6085\text{ft}^2$ .
Round Relative Error: Now, we need to find the absolute error, which is the difference between the actual area and the measured area. Absolute error = $|\text{Actual Area} - \text{Measured Area}|$ .Calculate the absolute error: $|100\text{ft}^2 - 94.3915\text{ft}^2| = 5.6085\text{ft}^2$ .To find the relative error, we divide the absolute error by the actual area. Relative error = \frac{\text{Absolute error}}{\text{Actual Area}}.
Round Relative Error: Now, we need to find the absolute error, which is the difference between the actual area and the measured area. Absolute error = $|\text{Actual Area} - \text{Measured Area}|$ .Calculate the absolute error: $|100\text{ft}^2 - 94.3915\text{ft}^2| = 5.6085\text{ft}^2$ .To find the relative error, we divide the absolute error by the actual area. Relative error = \frac{\text{Absolute error}}{\text{Actual Area}}.Perform the division to find the relative error: $\frac{5.6085\text{ft}^2}{100\text{ft}^2} = 0.056085$ .
Round Relative Error: Now, we need to find the absolute error, which is the difference between the actual area and the measured area. Absolute error = $|\text{Actual Area} - \text{Measured Area}|$ .Calculate the absolute error: $|100\text{ft}^2 - 94.3915\text{ft}^2| = 5.6085\text{ft}^2$ .To find the relative error, we divide the absolute error by the actual area. Relative error = \frac{\text{Absolute error}}{\text{Actual Area}}.Perform the division to find the relative error: $\frac{5.6085\text{ft}^2}{100\text{ft}^2} = 0.056085$ .Finally, we round the relative error to the nearest thousandth: $0.056085$ rounded to the nearest thousandth is $0.056$ .