Question

exercise 3: length of a pencil: 12.0 cm, 12.1 cm, 12.2 cm, 12.1 cm
a) find the average:
b) find the range:
c) find the random error:
d) write the result with the error:
e) percentage of uncertainty:

Explanation:

Part d)

Step1: Recall result and error

The average (result) is \( 12.1 \, \text{cm} \) and random error is \( 0.1 \, \text{cm} \).

Step2: Format result with error

Write as \( \text{Result} \pm \text{Error} \), so \( 12.1 \pm 0.1 \, \text{cm} \).

Part e)

Step1: Formula for % uncertainty

\( \% \text{Uncertainty} = \frac{\text{Error}}{\text{Result}} \times 100 \)

Step2: Substitute values

Error \( = 0.1 \, \text{cm} \), Result \( = 12.1 \, \text{cm} \).
\( \% \text{Uncertainty} = \frac{0.1}{12.1} \times 100 \approx 0.826\% \)

Answer:

(d): \( 12.1 \pm 0.1 \, \text{cm} \)