To find the percentage error when expressing \(\frac{2}{21}\) as a decimal to 2 decimal places (2d.p.), we first calculate its exact decimal value and then the value rounded to 2 decimal places.
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Calculate \(\frac{2}{21}\): \[ \frac{2}{21} \approx 0.09523809523809523 \dots \]
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Round to 2 decimal places: The value of \(\frac{2}{21}\) rounded to 2 decimal places is \(0.10\).
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Calculate the actual value: The actual value of \(\frac{2}{21}\) is approximately \(0.095238\).
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Find the error: We need to calculate the error between the rounded value and the actual value: \[ \text{Error} = \text{Rounded value} - \text{Actual value} = 0.10 - 0.095238 \approx 0.004762 \]
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Calculate the percentage error: The formula for percentage error is: \[ \text{Percentage Error} = \left(\frac{\text{Error}}{\text{Actual value}}\right) \times 100 \] Plugging in the values: \[ \text{Percentage Error} = \left(\frac{0.004762}{0.095238}\right) \times 100 \approx 5.0% \]
Therefore, the percentage error is approximately \(5.0%\).
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