Question

6.
You measure a piece of rope and find its length to be 13 m. Find the percent error of this measurement. Round to the nearest hundredth.


0.38%


3.85%


0.15%


0.92%

Answer 1

To calculate the percent error of a measurement, you can use the formula:

\[
\text{Percent Error} = \left( \frac{\text{Absolute Error}}{\text{True Value}} \right) \times 100
\]

However, to use this formula, we first need to define the "true value" and the "measured value." If we assume that the true length of the rope is indeed 13 m (or that there is some acceptable margin of error), we will need to know what that true value is or the error inherent in the measurement.

If you have no additional information indicating a true measurement or an accepted tolerance, we can't calculate the percent error since there is no absolute error defined.

Therefore, if we assume that the measured value of 13 m is indeed measured correctly and no error is specified, we cannot determine a percent error without that data. Please clarify if there's a reference or acceptable error value that we should use to calculate percent error.

In another context, if you had a slight error in measurement (for instance, +/- 0.05 m), the absolute error would be 0.05 m. In that case:

Using this as an example:
- Absolute error = 0.05 m
- True value (for calculation purposes) = 13 m

Calculating percent error:

\[
\text{Percent Error} = \left( \frac{0.05}{13} \right) \times 100 \approx 0.3846\%
\]

Rounding it to the nearest hundredth gives approximately 0.38%.

Without a specified error or true value, however, we can't produce a definitive percent error for the measurement of 13 m.