A measurement of 14.5 kg is recorded. Calculate: a) The absolute error. b) The percentage error. c) The tolerance.

The absolute error is half of the smallest unit of measurement.

$$\text{Absolute Error} = \frac{1}{2} \times 0.1 \text{ kg} = 0.05 \text{ kg}$$

The absolute error is $\boxed{\text{0.05 kg}}$.

$$\text{Percentage Error} = \frac{0.05 \text{ kg}}{14.5 \text{ kg}} \times 100\%$$ $$\text{Percentage Error} = 0.003448 \times 100\%$$ $$\text{Percentage Error} \approx 0.3448\%$$

Rounding to two decimal places, the percentage error is $\boxed{\text{0.34\%}}$.

Tolerance is the range within which the actual value lies, expressed as the measured value plus or minus the absolute error.

$$\text{Tolerance} = \text{Measured Value} \pm \text{Absolute Error}$$ $$\text{Tolerance} = 14.5 \text{ kg} \pm 0.05 \text{ kg}$$

This means the actual mass is between $14.5 - 0.05 = 14.45 \text{ kg}$ and $14.5 + 0.05 = 14.55 \text{ kg}$.
The tolerance is $\boxed{\text{14.5 kg} \pm \text{0.05 kg}}$.