Respuesta :
Answer:
So, the range of possible values for AB is 17.5 to 62.5, and the largest possible value is indeed 62.5, not 49. This range takes into account the uncertainties in both A and B and provides a reasonable estimation of the possible outcomes.
Step-by-step explanation:
In the given scenario, it seems there might be a misunderstanding regarding the calculation of uncertainties and how they relate to the possible range of values.
To calculate the uncertainty in the product AB, we need to consider the percentage uncertainties of A and B and propagate them through the multiplication. Let's go through the correct steps:
1. Calculate the percentage uncertainty of A:
Percentage uncertainty of A = (Absolute uncertainty of A / Value of A) * 100
Percentage uncertainty of A = (0.5 / 4) * 100 = 12.5%
2. Calculate the percentage uncertainty of B:
Percentage uncertainty of B = (Absolute uncertainty of B / Value of B) * 100
Percentage uncertainty of B = (1 / 10) * 100 = 10%
3. Calculate the uncertainty in the product AB:
Δ(AB) = (Percentage uncertainty of A + Percentage uncertainty of B) * (Value of A * Value of B) / 100
Δ(AB) = (12.5 + 10) * (4 * 10) / 100 = 22.5
Therefore, the correct result for AB, considering uncertainties, would be 40 ± 22.5.
Now, regarding the largest possible value, the calculated uncertainty does not suggest that 49 is the largest possible number. The ± 22.5 uncertainty represents the range of values within which the true value of AB is expected to lie with a certain level of confidence. In this case, it means that the true value of AB can be anywhere from 40 - 22.5 to 40 + 22.5.
So, the range of possible values for AB is 17.5 to 62.5, and the largest possible value is indeed 62.5, not 49. This range takes into account the uncertainties in both A and B and provides a reasonable estimation of the possible outcomes.
I hope this clarifies the confusion and helps you understand the correct approach to calculating uncertainties and their impact on the range of possible values.
Final answer:
The student is correct in calculating the percent uncertainty, but there is a misunderstanding in interpreting the calculated uncertainty as the largest possible value. The uncertainty represents the range within which the measurement is expected to fall, not the extremes.
Explanation:
calculating the percent uncertainty using the formula % unc = SA/A × 100%. However, there seems to be a misunderstanding in interpreting the calculated uncertainty as the largest possible value.
The uncertainty represents the range within which the measurement is expected to fall, not the extremes. The largest possible value is determined by adding the uncertainty to the expected value: 4 + 9 = 13, not 49.
Uncertainty in measurement is a concept that refers to the doubt or lack of confidence associated with the results of any measurement. No measurement is perfect, and there will always be some level of uncertainty associated with it.
This uncertainty arises from various sources, including limitations of the measuring instrument, the skill of the operator, and inherent variability in the quantity being measured.
Key points about uncertainty in measurement include:
Definition: Uncertainty is a parameter characterizing the dispersion of the values that could reasonably be attributed to a measured quantity. It is often expressed as an interval around the measured value, within which the true value is expected to lie with a certain level of confidence.
Sources of Uncertainty:
Instrumentation: The precision and accuracy of the measuring instrument contribute to uncertainty.
Environmental Conditions: Changes in temperature, pressure, or humidity can affect measurements.
Operator Skill: The skill and experience of the person making the measurement can introduce uncertainty.
Random Errors: Variability in repeated measurements.
