A rectangular plate has a length of (18.0 ± 0.2) cm and a width of (9.8 ± 0.1) cm. Calculate the area of the plate, including its uncertainty.
Correct all results to significant figures.
Please help someone
To calculate the area of the rectangular plate, you need to multiply its length by its width. Let's perform the calculation considering the given values:
Length of the plate, L = (18.0 ± 0.2) cm
Width of the plate, W = (9.8 ± 0.1) cm
To perform calculations with uncertainties, you need to consider the maximum possible value for one variable and the minimum possible value for the other variable. In this case, we will consider:
Max length = 18.0 + 0.2 = 18.2 cm
Min length = 18.0 - 0.2 = 17.8 cm
Max width = 9.8 + 0.1 = 9.9 cm
Min width = 9.8 - 0.1 = 9.7 cm
Now, let's calculate the area using the maximum and minimum values:
Max area = (18.2 cm) * (9.9 cm) = 180.18 cm²
Min area = (17.8 cm) * (9.7 cm) = 172.66 cm²
Now we have the maximum and minimum possible values for the area of the plate. To find the uncertainty, subtract the minimum value from the maximum value:
Uncertainty = Max area - Min area = 180.18 cm² - 172.66 cm² = 7.51 cm²
Finally, we express the result using the appropriate number of significant figures. Since both the length and width are given to three significant figures, we should round the area to three significant figures as well:
Area = 177 cm² (rounded to three significant figures)
Uncertainty = 8 cm² (rounded to one significant figure)
Therefore, the area of the plate is (177 ± 8) cm², including its uncertainty.