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

Explanation:

Percent error measures the difference between a claimed (experimental) value and the true/actual value relative to the actual value. First, find the absolute difference between the claimed and actual amounts to ensure the value is positive. Then divide this absolute difference by the actual amount, and multiply by 100 to get the percentage.

Answer:

To calculate percent error correctly:

1. Find the absolute value of the difference between the claimed amount and the actual amount: $| \text{Claimed Amount} - \text{Actual Amount} |$
2. Divide this absolute difference by the actual amount: $\frac{| \text{Claimed Amount} - \text{Actual Amount} |}{\text{Actual Amount}}$
3. Multiply the result by 100 to convert it to a percentage: $\frac{| \text{Claimed Amount} - \text{Actual Amount} |}{\text{Actual Amount}} \times 100$

The classmate's mistake was skipping the step of finding the absolute difference between the claimed and actual values, and instead directly dividing the claimed amount by the actual amount, which does not measure the error relative to the true value.