Sofia measured a line to be 8.9 inches long. If the actual length of the line is 8.7 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The correct answer and explanation is:
To find the percent error, use the formula: 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
Step-by-step:
- Measured Value = 8.9 inches
- Actual Value = 8.7 inches
∣Measured−Actual∣=∣8.9−8.7∣=0.2|\text{Measured} – \text{Actual}| = |8.9 – 8.7| = 0.2
Now plug this into the formula: Percent Error=(0.28.7)×100\text{Percent Error} = \left( \frac{0.2}{8.7} \right) \times 100 Percent Error=(0.02299)×100=2.29885\text{Percent Error} = (0.02299) \times 100 = 2.29885
Rounded to the nearest tenth, the percent error is: 2.3%\boxed{2.3\%}
Explanation (300 words):
Percent error is used to express how far a measured value is from the actual or true value in percentage form. It gives an idea of how accurate or inaccurate a measurement is. In this case, Sofia measured a line and got 8.9 inches, but the correct or actual length is 8.7 inches.
First, we calculate the difference between the measured value and the actual value, which is the absolute error. This comes out to 0.2 inches. The use of the absolute value ensures that the error is always positive, regardless of whether the measured value was higher or lower than the actual.
Next, we divide the error (0.2) by the actual value (8.7) to get the relative size of the error. This division gives us a decimal that we then multiply by 100 to convert it into a percentage. The result is about 2.29885 percent.
Finally, rounding this to the nearest tenth means we look at the digit in the hundredths place, which is 9. Since it is greater than or equal to 5, we round the tenths digit up, giving a final percent error of 2.3%.
This shows that Sofia’s measurement was 2.3% larger than the true value. Understanding percent error is especially important in science, engineering, and construction, where accuracy matters. It helps determine how trustworthy a measurement is and whether the error is within acceptable limits.