Question

Greta is mailing a care package to her little sister at college. After packing the box, she weighs it on her bathroom scale to estimate the mailing cost. The scale shows the package weighing 3 pounds. At the post office, the clerk weighs the package on a more precise scale, and it weighs 3.25 pounds. What is the percent error for Greta's scale's measurement?
If necessary, round your answer to the nearest tenth of a percent.
___%

Answer 1

To calculate the percent error for Greta's scale, we can use the following formula:

\[
\text{Percent Error} = \left( \frac{\text{Absolute Error}}{\text{True Value}} \right) \times 100
\]

Where:
- Absolute Error is the difference between the measured value and the true value.
- True Value is the actual weight of the package.

1. **Determine the measurements**:
- Greta's measurement (measured value) = 3 pounds
- True value (weight from the post office) = 3.25 pounds

2. **Calculate the Absolute Error**:
\[
\text{Absolute Error} = | \text{Measured Value} - \text{True Value} | = | 3 - 3.25 | = 0.25 \text{ pounds}
\]

3. **Calculate the Percent Error**:
\[
\text{Percent Error} = \left( \frac{0.25}{3.25} \right) \times 100
\]

4. **Perform the calculation**:
\[
\text{Percent Error} = \left( \frac{0.25}{3.25} \right) \times 100 = 0.076923 \times 100 \approx 7.6923\%
\]

5. **Round to the nearest tenth of a percent**:
7.6923% rounded to the nearest tenth is 7.7%.

Thus, the percent error for Greta's scale's measurement is **7.7%**.