Final answer:
To calculate the uncertainty of a ratio of two measurements with known uncertainties, add the percent uncertainties of both measurements and apply this sum as the percent uncertainty to the calculated ratio.
Step-by-step explanation:
If you have a ratio of two measurements with known uncertainties, you can calculate the uncertainty of the ratio by using the method of adding percent uncertainties. This method is applicable when the uncertainties in the measurements involved are small (a few percent or less).
For example, let's say you have two values A and B with uncertainties of 2% and 1%, respectively. If you were to calculate the ratio A/B, the percent uncertainty in the resulting ratio would be the sum of the individual percent uncertainties, which in this case is 2% + 1% = 3%. The actual uncertainty of the ratio can then be calculated by multiplying the result of A/B by 3%.
Consider a practical scenario where a floor has a length of 4.00 m with an uncertainty of 2% and a width of 3.00 m with an uncertainty of 1%. The calculated area of the floor would be 4.00 m * 3.00 m = 12.0 m². The total uncertainty for the area, based on the percent uncertainty method, would be 2% + 1% = 3%, which equates to an uncertainty value of 12.0 m² * 0.03 = 0.36 m², and this would be rounded to 0.4 m² due to significant figures.