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Eric measures a line to be 5.46 in long. If the actual measurement is 5 in, find Eric's relative error to the nearest hundredth. Answer:

Eric measures a line to be 55.4646 in long. If the actual measurement is 55 in, find Eric's relative error to the nearest hundredth.\newlineAnswer:

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Full solution

Q. Eric measures a line to be 55.4646 in long. If the actual measurement is 55 in, find Eric's relative error to the nearest hundredth.\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. \newlineAbsolute error = ∣Measured value−Actual value∣|\text{Measured value} - \text{Actual value}|
  2. Find Absolute Error: Now we calculate the absolute error using the values given. Absolute error = ∣5.46 in−5 in∣=∣0.46 in∣=0.46 in|5.46 \text{ in} - 5 \text{ in}| = |0.46 \text{ in}| = 0.46 \text{ in}
  3. Calculate Relative Error: Next, we find the relative error by dividing the absolute error by the actual measurement.\newlineRelative error = Absolute errorActual value\frac{\text{Absolute error}}{\text{Actual value}}
  4. Perform Division: We perform the division to find the relative error.\newlineRelative error = 0.46 in/5 in=0.0920.46 \, \text{in} / 5 \, \text{in} = 0.092
  5. Round Relative Error: Finally, we round the relative error to the nearest hundredth as asked in the question prompt.\newlineRelative error (rounded) = 0.090.09

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