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Alex measures a line to be 6.68ft long. If the actual measurement is 7ft, find Alex's relative error to the nearest hundredth. Answer:

Alex measures a line to be 6.68ft 6.68 \mathrm{ft} long. If the actual measurement is 7ft 7 \mathrm{ft} , find Alex's relative error to the nearest hundredth.\newlineAnswer:

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Full solution

Q. Alex measures a line to be 6.68ft 6.68 \mathrm{ft} long. If the actual measurement is 7ft 7 \mathrm{ft} , find Alex's relative error to the nearest hundredth.\newlineAnswer:
  1. Understand relative error: Understand the concept of relative error. Relative error is the absolute error divided by the actual measurement, often expressed as a percentage. The absolute error is the difference between the measured value and the actual value.
  2. Calculate absolute error: Calculate the absolute error.\newlineAbsolute error = ∣Measured Value−Actual Value∣|\text{Measured Value} - \text{Actual Value}|\newlineAbsolute error = ∣6.68ft−7ft∣|6.68\text{ft} - 7\text{ft}|\newlineAbsolute error = ∣−0.32ft∣|-0.32\text{ft}|\newlineAbsolute error = 0.32ft0.32\text{ft}
  3. Calculate relative error: Calculate the relative error.\newlineRelative error = (Absolute error/Actual Value)×100(\text{Absolute error} / \text{Actual Value}) \times 100 (to get a percentage)\newlineRelative error = (0.32 ft/7 ft)×100(0.32\,\text{ft} / 7\,\text{ft}) \times 100\newlineRelative error = 0.04571428571×1000.04571428571 \times 100\newlineRelative error = 4.571428571%4.571428571\%
  4. Round relative error: Round the relative error to the nearest hundredth.\newlineRelative error (rounded) = 4.57%4.57\%

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