the dimensions of a rectangle are measured and given as 6.9 cm and 3.06 cm, calculate to 4 s.f. the percentage error in the area
Well, let's calculate the area of the rectangle with the given dimensions: 6.9 cm * 3.06 cm = 21.114 cm².
Now, let's find the percentage error in the area. We need to calculate the difference between the actual area and the measured area, and then divide that by the actual area and multiply by 100.
The actual area would be calculated with the exact measurements, which we don't have here. So, let's just assume the given measurements are accurate for now.
Percentage error = ((21.114 cm² - 21.11 cm²) / 21.114 cm²) * 100.
Now, assuming you meant "4 s.f." as "to 4 significant figures," we need to round our answer to 4 significant figures.
Percentage error = ((0.004 cm² / 21.114 cm²) * 100) = 0.01896... * 100 = 1.9%.
So, the percentage error in the area of the rectangle is approximately 1.9%.
To calculate the percentage error in the area, we need to find the difference between the measured area and the actual area, and then express it as a percentage of the actual area.
First, let's calculate the measured area:
Measured Area = Length × Width
Length = 6.9 cm (given)
Width = 3.06 cm (given)
Measured Area = 6.9 cm × 3.06 cm = 21.114 cm²
Now, let's calculate the actual area:
Actual Area = Actual Length × Actual Width
To calculate the actual area, we need to know the measurements of the rectangle without any errors. Since this information is not provided, we cannot calculate the actual area accurately. However, for the sake of calculation, let's assume the actual length and width as 7 cm and 3 cm respectively.
Actual Length = 7 cm
Actual Width = 3 cm
Actual Area = 7 cm × 3 cm = 21 cm²
Now, let's find the difference between the measured area and the actual area:
Difference = Measured Area - Actual Area
Difference = 21.114 cm² - 21 cm²
Difference = 0.114 cm²
Finally, let's calculate the percentage error:
Percentage Error = (Difference / Actual Area) × 100
Percentage Error = (0.114 cm² / 21 cm²) × 100
Percentage Error ≈ 0.543%
Therefore, the percentage error in the area of the rectangle is approximately 0.543%.