To find the percentage error when expressing \( \frac{2}{21} \) as a decimal to 2 decimal places (2d.p.), we first need to calculate the actual value of \( \frac{2}{21} \) and then the value rounded to 2 decimal places.
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Calculate \( \frac{2}{21} \): \[ \frac{2}{21} \approx 0.09523809523809523 \]
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Round \( 0.09523809523809523 \) to 2 decimal places: \[ 0.095 \text{ rounds to } 0.10 \text{ (to 2d.p.)} \]
Now we have:
- Actual value: \( 0.095238 \)
- Rounded value (to 2d.p.): \( 0.10 \)
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Calculate the error: \[ \text{Error} = \text{Rounded value} - \text{Actual value} = 0.10 - 0.095238 \approx 0.004762 \]
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Calculate the percentage error: \[ \text{Percentage Error} = \left( \frac{\text{Error}}{\text{Actual value}} \right) \times 100 \] \[ \text{Percentage Error} = \left( \frac{0.004762}{0.095238} \right) \times 100 \approx 5% \]
Thus, the percentage error is approximately 5%.
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