Jacob measured a line to be 6 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?
The correct answer and explanation is:
Correct Answer: 6.3%
Explanation:
Percent error is a way of expressing how inaccurate a measurement is compared to the actual or true value. It helps to understand how far off a measured value is from what it should be. The formula for calculating percent error is: Percent Error=(∣Measured Value−Actual Value∣Actual Value)×100\text{Percent Error} = \left( \frac{|\text{Measured Value} – \text{Actual Value}|}{\text{Actual Value}} \right) \times 100
In this case:
- Measured value = 6 inches
- Actual value = 6.4 inches
First, find the absolute difference between the measured and actual value: ∣6−6.4∣=0.4|6 – 6.4| = 0.4
Now divide this difference by the actual value: 0.46.4=0.0625\frac{0.4}{6.4} = 0.0625
Multiply by 100 to convert to a percentage: 0.0625×100=6.25%0.0625 \times 100 = 6.25\%
Now round to the nearest tenth of a percent: 6.25%≈6.3%6.25\% \approx 6.3\%
So, the percent error is 6.3 percent.
Understanding percent error is important in many scientific and mathematical applications. It shows how much a measurement deviates from a known or true value, helping to evaluate the reliability of data. In this example, Jacob’s measurement of the line was reasonably close, but still off by 0.4 inches. When converted to a percent error, the deviation is 6.3 percent, which may or may not be acceptable depending on the level of precision required for the task. If the measurement needed to be highly accurate, this percent error might be considered too large. If the context allowed for some tolerance, then the measurement might still be useful.