Question

1. error analysis a classmate says that to calculate the percent error, you divide the claimed amount by the actual amount, then multiply by 100. explain how to correctly calculate the percent error.

Explanation:

First, find the absolute difference between the claimed (measured) amount and the actual (accepted) amount to get the absolute error. Then divide this absolute error by the actual amount, and finally multiply by 100 to convert the result to a percentage. This accounts for the deviation relative to the true value, which the classmate's method failed to do (they skipped finding the difference between the two values).

Answer:

To correctly calculate percent error:

1. Find the absolute error: $|\text{Claimed Amount} - \text{Actual Amount}|$
2. Divide the absolute error by the actual amount: $\frac{|\text{Claimed Amount} - \text{Actual Amount}|}{\text{Actual Amount}}$
3. Multiply the result by 100: $\frac{|\text{Claimed Amount} - \text{Actual Amount}|}{\text{Actual Amount}} \times 100$

This gives the percent error, which measures the relative difference between the claimed and actual value as a percentage.