To find Alex's relative error, we first need to calculate the absolute error and then divide that by the actual measurement.
-
Calculate the absolute error: \[ \text{Absolute error} = \text{Measured value} - \text{Actual value} = 6.42 \text{ ft} - 6 \text{ ft} = 0.42 \text{ ft} \]
-
Calculate the relative error: \[ \text{Relative error} = \frac{\text{Absolute error}}{\text{Actual value}} = \frac{0.42 \text{ ft}}{6 \text{ ft}} \]
-
Compute the relative error: \[ \text{Relative error} = \frac{0.42}{6} = 0.07 \]
-
Convert to a percentage (optional step, often done in practical applications): \[ \text{Relative error (percentage)} = 0.07 \times 100 = 7% \]
-
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 \(\boxed{0.070}\).