Final answer:
The empirical propagation method is used to find the uncertainty in the area when measurements with uncertainties are multiplied or divided. In this case, the length is (10 ± 1)mm and the width is (5 ± 1)mm. The uncertainty in the area is found by adding the percent uncertainties in the measurements and multiplying it by the area.
Step-by-step explanation:
The empirical propagation method is used to find the uncertainty in the area when measurements with uncertainties are multiplied or divided. In this case, the length is (10 ± 1)mm and the width is (5 ± 1)mm.
To find the uncertainty in area, we use the sum of the percent uncertainties in the measurements. The percent uncertainty in the length is 1/10 * 100 = 10%, and the percent uncertainty in the width is 1/5 * 100 = 20%. We add these percentages together to get 10% + 20% = 30%.
Now, we can calculate the area by multiplying the length and width: 10mm * 5mm = 50mm². The uncertainty in the area is 30% of the area, so the uncertainty is 30/100 * 50mm² = 15mm².