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Alex measures a line to be 6.43cm long. If the actual measurement is 6cm, find Alex's relative error to the nearest hundredth. Answer:

Alex measures a line to be 6.43 cm 6.43 \mathrm{~cm} long. If the actual measurement is 6 cm 6 \mathrm{~cm} , find Alex's relative error to the nearest hundredth.\newlineAnswer:

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Full solution

Q. Alex measures a line to be 6.43 cm 6.43 \mathrm{~cm} long. If the actual measurement is 6 cm 6 \mathrm{~cm} , find Alex'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.\newlineCalculation: Absolute error = ∣Measured value−Actual value∣=∣6.43 cm−6 cm∣=0.43 cm|\text{Measured value} - \text{Actual value}| = |6.43\,\text{cm} - 6\,\text{cm}| = 0.43\,\text{cm}
  2. Calculate Relative Error: Now we need to calculate the relative error by dividing the absolute error by the actual measurement.\newlineCalculation: Relative error = Absolute errorActual value=0.43 cm6 cm\frac{\text{Absolute error}}{\text{Actual value}} = \frac{0.43\,\text{cm}}{6\,\text{cm}}
  3. Perform Division: Perform the division to find the relative error.\newlineCalculation: Relative error = 0.43 cm6 cm≈0.071666...\frac{0.43\,\text{cm}}{6\,\text{cm}} \approx 0.071666...
  4. Round to Nearest Hundredth: To express the relative error to the nearest hundredth, we round the result to two decimal places.\newlineCalculation: Relative error ≈0.07\approx 0.07 (to the nearest hundredth)

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