Final answer:
To calculate percent uncertainty, divide the absolute uncertainty by the average value and then multiply by 100%. For a bag of apples weighing 5.1 lbs with an uncertainty of 0.3 lbs, the percent uncertainty is approximately 5.882%. Percent uncertainty indicates the precision of a measurement.
Step-by-step explanation:
The question concerns percent uncertainty in a measurement. Percent uncertainty is a way to quantify the precision of a measurement by comparing the magnitude of its uncertainty to the magnitude of its value. To calculate the percent uncertainty, you divide the absolute uncertainty by the average value and then multiply by 100% to convert to a percentage. Given the average weight of a bag of apples (A) is 5.1 lbs and the uncertainty (ΔA) is 0.3 lbs, the percent uncertainty would be (ΔA / A) × 100%.
Using the formula for percent uncertainty:
- Percent Uncertainty = (ΔA / A) × 100%
- Percent Uncertainty = (0.3 lbs / 5.1 lbs) × 100%
- Percent Uncertainty = 0.05882 × 100%
- Percent Uncertainty = 5.882%
To find the significance of this measurement, we note that if the weight of the bag were to be halved while keeping the uncertainty the same, the percent uncertainty would double. This illustrates that as the weight decreases, its relative uncertainty has more significance in comparison to its actual weight.