Question

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

Answer 1

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 \(5.0\%\).