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David measures a line to be 4.48ft long. If the actual measurement is 4ft, find David's relative error to the nearest hundredth. Answer:

David measures a line to be 4.48ft 4.48 \mathrm{ft} long. If the actual measurement is 4ft 4 \mathrm{ft} , find David's relative error to the nearest hundredth.\newlineAnswer:

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Full solution

Q. David measures a line to be 4.48ft 4.48 \mathrm{ft} long. If the actual measurement is 4ft 4 \mathrm{ft} , find David'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∣|\text{Measured value} - \text{Actual value}|\newlineAbsolute error = ∣4.48ft−4ft∣|4.48\text{ft} - 4\text{ft}|\newlineAbsolute error = ∣0.48ft∣|0.48\text{ft}|
  2. Find Relative Error: Now that we have the absolute error, we can find the relative error by dividing the absolute error by the actual measurement.\newlineCalculation: Relative error = Absolute errorActual measurement\frac{\text{Absolute error}}{\text{Actual measurement}}\newlineRelative error = 0.48 ft4 ft\frac{0.48\,\text{ft}}{4\,\text{ft}}\newlineRelative error = 0.120.12
  3. Round to Nearest Hundredth: To express the relative error to the nearest hundredth, we need to round the result to two decimal places.\newlineCalculation: Rounded relative error = 0.120.12 (It is already at the hundredth place, so no further rounding is needed.)

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