Question: User: Sofia measured a line to be $6.7$ inches long. If the actual length of the line is $6.4$ inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
1. **State the problem:**
We need to find the percent error of Sofia's measurement of a line.
2. **Formula for percent error:**
$$\text{Percent Error} = \left| \frac{\text{Measured Value} - \text{Actual Value}}{\text{Actual Value}} \right| \times 100\%$$
3. **Identify values:**
Measured Value = $6.7$ inches
Actual Value = $6.4$ inches
4. **Calculate the difference:**
$$6.7 - 6.4 = 0.3$$
5. **Calculate the fraction:**
$$\frac{0.3}{6.4}$$
6. **Simplify the fraction:**
$$\frac{0.3}{6.4} = \frac{\cancel{0.3}}{\cancel{6.4}}$$ (no common factors to cancel, so fraction remains as is)
7. **Calculate the decimal:**
$$\frac{0.3}{6.4} = 0.046875$$
8. **Convert to percent:**
$$0.046875 \times 100\% = 4.6875\%$$
9. **Round to nearest tenth:**
$$4.7\%$$
**Final answer:** The percent error of the measurement is approximately $4.7\%$.