Sophie measured a piece of paper to be 21.7 cm by 28.5 cm. The piece of paper is actually 21.6 cm by 28.4 cm.
Determine the amount of square centimeters in the area of the piece of paper using Sophie's measurements.(I got 618.45 sq cm)
Determine the number of square centimeters in the actual area of the piece of paper. (I got 613.44 sq cm.)
Determine the relative error in calculating the area. Express your answer as a decimal to the nearest thousandth. (I don't know how to do this part.)
You computed the measured area, 618.45 cm^2, correctly.
The true actual area, 613.44 cm^2, is also correct.
The relative error is
(measured-actual)/actual = 5.01/613.44 0.008167 = 0.008 (to the nearest thousandth)
thanks
To determine the relative error in calculating the area, follow these steps:
1. Calculate the difference in the areas: Subtract the calculated area (618.45 sq cm) from the actual area (613.44 sq cm):
Actual area - Calculated area = 613.44 sq cm - 618.45 sq cm = -5.01 sq cm
2. Take the absolute value of the difference: Since the result is negative (-5.01 sq cm), take the absolute value to ignore the sign:
Absolute value of the difference = |-5.01| = 5.01 sq cm
3. Calculate the relative error: Divide the absolute difference by the actual area, and then multiply by 100 to express it as a percentage:
Relative error = (Absolute difference / Actual area) * 100 = (5.01 sq cm / 613.44 sq cm) * 100
Now, let's perform the calculation:
Relative error = (5.01 sq cm / 613.44 sq cm) * 100 ≈ 0.816%
Therefore, the relative error in calculating the area is approximately 0.816% (expressed as a decimal to the nearest thousandth).