Instead of expressing 2 all over 21 as a decimal number to 2s.f, a student expressed it to 2d.p. find 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 need to calculate the actual value of \( \frac{2}{21} \) and then the value rounded to 2 decimal places.

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

  2. 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.): \( 0.10 \)
  1. Calculate the error: \[ \text{Error} = \text{Rounded value} - \text{Actual value} = 0.10 - 0.095238 \approx 0.004762 \]

  2. 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%.