Instead of expressing 2 all over 21 as a decimal number to 2s.f, a student expressed it to 2d. P. Fine the percentage error

1 answer

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.

  1. Calculate \(\frac{2}{21}\): \[ \frac{2}{21} \approx 0.09523809523809523 \dots \]

  2. Round to 2 decimal places: The value of \(\frac{2}{21}\) rounded to 2 decimal places is \(0.10\).

  3. Calculate the actual value: The actual value of \(\frac{2}{21}\) is approximately \(0.095238\).

  4. Find the error: We need to calculate the error between the rounded value and the actual value: \[ \text{Error} = \text{Rounded value} - \text{Actual value} = 0.10 - 0.095238 \approx 0.004762 \]

  5. 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 \(5.0%\).