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Bob measures a line to be 2.4 in long. If the actual measurement is 2 in, find Bob's relative error to the nearest thousandth. Answer:

Bob measures a line to be 22.44 in long. If the actual measurement is 22 in, find Bob's relative error to the nearest thousandth.\newlineAnswer:

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Q. Bob measures a line to be 22.44 in long. If the actual measurement is 22 in, find Bob's relative error to the nearest thousandth.\newlineAnswer:
  1. Calculate Absolute Error: To find the relative error, we need to calculate the absolute error and then divide it by the actual measurement. The absolute error is the difference between the measured value and the actual value.\newlineCalculation: Absolute error = ∣Measured value−Actual value∣=∣2.4 in−2 in∣=0.4 in|\text{Measured value} - \text{Actual value}| = |2.4 \, \text{in} - 2 \, \text{in}| = 0.4 \, \text{in}
  2. Find Relative Error: Now we need to find the relative error by dividing the absolute error by the actual measurement.\newlineCalculation: Relative error = Absolute errorActual measurement=0.4 in2 in=0.2\frac{\text{Absolute error}}{\text{Actual measurement}} = \frac{0.4 \, \text{in}}{2 \, \text{in}} = 0.2
  3. Round to Nearest Thousandth: To express the relative error to the nearest thousandth, we need to round the result to three decimal places.\newlineCalculation: Rounded relative error = 0.2000.200 (to the nearest thousandth)

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