Final answer:
To calculate percent uncertainty, divide the uncertainty by the average weight and multiply by 100%. The percent uncertainty of a 5.1 lb bag of apples with ± 0.3 lb uncertainty is approximately 6%. If the bag's weight was half, with the same uncertainty, the percent uncertainty would double to approximately 11.76%.
Step-by-step explanation:
The weight of a full-body protective apron with 1 mm lead equivalent is asked in the question. Given the context of weights and measures, we will review the concept of percent uncertainty in relation to a specific example of a bag of apples that is determined to weigh 5.1 ± 0.3 lb. This variance provides us with a percent uncertainty which is a way of expressing the precision of a measurement. To find the percent uncertainty, we divide the range of uncertainty (0.3 lb) by the average weight (5.1 lb) and multiply by 100% to convert it to a percentage.
Percent Uncertainty = ±(range / average weight) × 100%
±(0.3 lb / 5.1 lb) × 100% ≈ 5.88%, which we could round to approximately 6%.
If the weight of the bag of apples were to be half as heavy (2.55 lbs) with the same uncertainty in weight (0.3 lb), the percent uncertainty would increase. Using the same formula, we find:
Percent Uncertainty for Half Weight = ±(range / (average weight / 2)) × 100%
±(0.3 lb / 2.55 lb) × 100% ≈ 11.76%, which is greater than the percent uncertainty for the 5.1 lb weight, showing that the relative uncertainty becomes larger as the measured weight becomes smaller while the absolute uncertainty remains the same.