Question

Camila measured a line to be 17.5 inches long. If the actual length of the line is 18.5 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

Answer 1

To calculate the percent error of Camila's measurement, we can use the formula for percent error:

\[
\text{Percent Error} = \left( \frac{|\text{Measured Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100
\]

In this case:
- Measured Value = 17.5 inches
- Actual Value = 18.5 inches

First, we find the absolute error:

\[
|\text{Measured Value} - \text{Actual Value}| = |17.5 - 18.5| = |-1.0| = 1.0 \text{ inches}
\]

Next, we substitute the absolute error and the actual value into the percent error formula:

\[
\text{Percent Error} = \left( \frac{1.0}{18.5} \right) \times 100
\]

Now, we will compute the fraction:

\[
\frac{1.0}{18.5} \approx 0.054054
\]

Now, multiply by 100 to get the percent error:

\[
0.054054 \times 100 \approx 5.4054
\]

Rounding to the nearest tenth of a percent:

\[
\text{Percent Error} \approx 5.4\%
\]

Thus, the percent error of the measurement is

\[
\boxed{5.4\%}
\]