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Carter measures a line to be 9.33cm long. If the actual measurement is 9cm, find Carter's relative error to the nearest hundredth. Answer:

Carter measures a line to be 9.33 cm 9.33 \mathrm{~cm} long. If the actual measurement is 9 cm 9 \mathrm{~cm} , find Carter's relative error to the nearest hundredth.\newlineAnswer:

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Q. Carter measures a line to be 9.33 cm 9.33 \mathrm{~cm} long. If the actual measurement is 9 cm 9 \mathrm{~cm} , find Carter'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 = ∣9.33cm−9cm∣|9.33\text{cm} - 9\text{cm}|\newlineAbsolute error = ∣0.33cm∣|0.33\text{cm}|\newlineAbsolute error = 0.33cm0.33\text{cm}
  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 = (0.33 cm/9 cm)×100(0.33\,\text{cm} / 9\,\text{cm}) \times 100\newlineRelative error = 0.036666...×1000.036666... \times 100\newlineRelative error = 3.6666...%3.6666...\%
  4. Round relative error: Round the relative error to the nearest hundredth.\newlineRelative error (rounded) = 3.67%3.67\%

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