Try It! The specification for the length of a bolt is 4.75 inches. A machinist makes a bolt that is 4.769 inches long. What is the percent error of the bolt's length?

To calculate the percent error, you first find the difference between the specified length and the actual length of the bolt. This would be \( 4.75 - 4.769 = -0.019 \) inches. Taking the absolute value gives you \( 0.019 \) inches. Then, divide this difference by the specified length: \( \frac{0.019}{4.75} \approx 0.004 \). Finally, multiply by 100 to convert it to a percentage: \( 0.004 \times 100 = 0.4\% \). So, the percent error of the bolt's length is 0.4%. Achieving precision in manufacturing is crucial, especially in industries like aerospace or automotive, where even a slight deviation can lead to substantial issues. Understanding concepts like percent error helps machinists and engineers ensure they meet specifications, preventing costly mistakes and maintaining quality control. Being aware of tolerances and how to monitor them can lead to more robust designs and safer products—safety first!