Question

Alex measures a line to be 6.42 ft long. If the actual measurement is 6 ft, find Alex's relative error to the nearest thousandth.

Answer 1

To find Alex's relative error, we first need to calculate the absolute error and then divide that by the actual measurement.

1. **Calculate the absolute error**:
\[
\text{Absolute error} = \text{Measured value} - \text{Actual value} = 6.42 \text{ ft} - 6 \text{ ft} = 0.42 \text{ ft}
\]

2. **Calculate the relative error**:
\[
\text{Relative error} = \frac{\text{Absolute error}}{\text{Actual value}} = \frac{0.42 \text{ ft}}{6 \text{ ft}}
\]

3. **Compute the relative error**:
\[
\text{Relative error} = \frac{0.42}{6} = 0.07
\]

4. **Convert to a percentage** (optional step, often done in practical applications):
\[
\text{Relative error (percentage)} = 0.07 \times 100 = 7\%
\]

5. **Round to the nearest thousandth**:
Since the relative error as a decimal is \(0.07\), the relative error rounded to the nearest thousandth is \(0.070\).

Thus, Alex's relative error is \(\boxed{0.070}\).