The actual dimensions of a rectangle are 9ft by 6ft. Eric measures the sides to be 8.91ft by 6.22ft. In calculating the area, what is the relative error, to the nearest hundredth.Answer:
Q. The actual dimensions of a rectangle are 9ft by 6ft. Eric measures the sides to be 8.91ft by 6.22ft. 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 = 9ft×6ft.
Calculate actual area: Perform the calculation for the actual area. Actual area = 9ft×6ft=54ft2.
Calculate measured area: Calculate the measured area of the rectangle using the measured dimensions. Measured area = 8.91ft×6.22ft.
Calculate measured area: Perform the calculation for the measured area. Measured area = 8.91ft×6.22ft≈55.43ft2.
Calculate absolute error: Calculate the absolute error by subtracting the actual area from the measured area. Absolute error = ∣Measured area−Actual area∣.
Calculate absolute error: Perform the calculation for the absolute error. Absolute error = ∣55.43ft2−54ft2∣≈1.43ft2.
Calculate relative error: Calculate the relative error by dividing the absolute error by the actual area.Relative error = Actual areaAbsolute error.
Calculate relative error: Perform the calculation for the relative error. Relative error = 54ft21.43ft2≈0.02648.
Convert relative error: Convert the relative error to a percentage and round to the nearest hundredth.Relative error (percentage) = 0.02648×100≈2.65%.