The question in the image reads:

The accepted length of a tool is 485 millimeters (mm). During an inspection, an engineer measured one of her tools to ensure that it fit within the allowable error range. She measured it at 650 millimeters. What was the percentage of error, rounded to the nearest hundredth percent?

Step-by-step Solution:

1. Formula for Percentage Error: $\text{Percentage Error} = \left| \frac{\text{Measured Value} - \text{Accepted Value}}{\text{Accepted Value}} \right| \times 100$

2. Substitute the Values: $\text{Measured Value} = 650, \quad \text{Accepted Value} = 485$ Substituting these: $\text{Percentage Error} = \left| \frac{650 - 485}{485} \right| \times 100$

3. Perform the Calculation: $\text{Percentage Error} = \left| \frac{165}{485} \right| \times 100$ Simplify the fraction: $\frac{165}{485} \approx 0.3402$ Multiply by 100: $0.3402 \times 100 \approx 34.02\%$

4. Final Answer: The percentage error is 34.02%.

Would you like me to explain anything in more detail?

Related Questions:

1. How is percentage error used in quality control processes?
2. What happens if the percentage error is negative? Does it affect accuracy?
3. How does this calculation differ for relative versus absolute error?
4. Could this percentage error indicate a problem with the measurement tool?
5. What other real-life situations require percentage error calculations?

Tip:

Always compare both the measurement and standard value carefully to ensure your error calculations make sense in context!