To find the percent error of the bolt's length, we use the formula:

$\text{Percent Error} = \left| \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right| \times 100$

Given:

• True Value (Specification): $4.75 \, \text{inches}$
• Measured Value: $4.769 \, \text{inches}$

Substitute the values into the formula:

$\text{Percent Error} = \left| \frac{4.769 - 4.75}{4.75} \right| \times 100$

First, calculate the difference:

$4.769 - 4.75 = 0.019$

Then divide by the true value:

$\frac{0.019}{4.75} \approx 0.004$

Finally, multiply by 100 to convert to a percentage:

$0.004 \times 100 = 0.4\%$

Final Answer:

The percent error of the bolt's length is approximately 0.4%.

Would you like a step-by-step breakdown or have additional questions?

Related Questions:

1. How does the percent error change if the true value increases or decreases?
2. Can the percent error ever be negative? Why or why not?
3. How does the precision of the measured value affect the accuracy of the percent error calculation?
4. What is the acceptable range of percent error in industrial manufacturing for bolts like this?
5. How can the machinist reduce the error when creating future bolts?

Tip:

Always ensure that the measured and true values have consistent units before calculating percent error.