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Eric measures a line to be 7.3ft long. If the actual measurement is 7ft, find Eric's relative error to the nearest hundredth. Answer:

Eric measures a line to be 7.3ft 7.3 \mathrm{ft} long. If the actual measurement is 7ft 7 \mathrm{ft} , find Eric's relative error to the nearest hundredth.\newlineAnswer:

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Full solution

Q. Eric measures a line to be 7.3ft 7.3 \mathrm{ft} long. If the actual measurement is 7ft 7 \mathrm{ft} , 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 = ∣7.3 ft−7 ft∣=∣0.3 ft∣=0.3 ft|7.3\,\text{ft} - 7\,\text{ft}| = |0.3\,\text{ft}| = 0.3\,\text{ft}
  3. Calculate Relative Error: Next, we calculate the relative error by dividing the absolute error by the actual measurement.\newlineRelative error = Absolute errorActual measurement\frac{\text{Absolute error}}{\text{Actual measurement}}
  4. Perform Division: Now we perform the calculation using the values we have.\newlineRelative error = 0.3 ft7 ft\frac{0.3\,\text{ft}}{7\,\text{ft}}
  5. Calculate Relative Error: Performing the division gives us the relative error. Relative error = 0.042857…0.042857\ldots
  6. Round to Nearest Hundredth: Finally, we round the relative error to the nearest hundredth as asked in the question prompt.\newlineRelative error (rounded to the nearest hundredth) = 0.040.04

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