The actual dimensions of a rectangle are 3cm by 7cm. Carter measures the sides to be 3.17cm by 7.32cm. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Question

The actual dimensions of a rectangle are  3cm by  7cm. Carter measures the sides to be  3.17cm by  7.32cm. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Bytelearn · Accepted Answer

Calculate Actual Area: Calculate the actual area of the rectangle. The formula for the area of a rectangle is length × width. Actual area = 3cm × 7cm.Calculate Actual Area: Perform the calculation for the actual area. Actual area = 21 cm².Calculate Measured Area: Calculate the measured area of the rectangle using Carter's measurements. Measured area = 3.17cm × 7.32cm.Calculate Measured Area: Perform the calculation for the measured area. Measured area ≈ 23.2044 cm² (rounded to four decimal places for precision in later calculations).Calculate Absolute Error: Calculate the absolute error. Absolute error = |Measured area - Actual area|. Absolute error ≈ |23.2044 cm² - 21 cm²|.Calculate Absolute Error: Perform the calculation for the absolute error. Absolute error ≈ 2.2044 cm².Calculate Relative Error: Calculate the relative error. Relative error = (Absolute error / Actual area).Calculate Relative Error: Perform the calculation for the relative error. Relative error ≈ (2.2044 cm² / 21 cm²).Convert Relative Error: Convert the relative error to a decimal rounded to the nearest thousandth. Relative error ≈ 0.105 (rounded to three decimal places).Convert Relative Error: Convert the decimal to a percentage by multiplying by 100. Relative error percentage ≈ 0.105 × 100.Calculate Relative Error Percentage: Perform the calculation for the relative error percentage. Relative error percentage ≈ 10.5%.

The actual dimensions of a rectangle are $3 \mathrm{~cm}$ by $7 \mathrm{~cm}$ . Carter measures the sides to be $3.17 \mathrm{~cm}$ by $7.32 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer:

Full solution

More problems from Percent error: word problems

Related topics

The actual dimensions of a rectangle are 3 cm 3 \mathrm{~cm} 3 cm by 7 cm 7 \mathrm{~cm} 7 cm. Carter measures the sides to be 3.17 cm 3.17 \mathrm{~cm} 3.17 cm by 7.32 cm 7.32 \mathrm{~cm} 7.32 cm. In calculating the area, what is the relative error, to the nearest thousandth.\newlineAnswer:

The actual dimensions of a rectangle are $3 \mathrm{~cm}$ by $7 \mathrm{~cm}$ . Carter measures the sides to be $3.17 \mathrm{~cm}$ by $7.32 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer: