1. State the problem: We need to calculate the percentage error of a measurement of the value of a ball given to the nearest centimeter. 2. Recall the formula for percentage error: $$\text{Percentage Error} = \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \times 100$$ 3. Identify the true value and the measured value. Since the measurement is to the nearest cm, the maximum possible error is $\pm 0.5$ cm. 4. If the measurement is $M$ cm, the range of true value is $M - 0.5$ to $M + 0.5$ cm. The maximum error is $0.5$ cm. 5. Calculate the percentage error using the maximum error: $$\text{Percentage Error} = \frac{0.5}{M} \times 100$$ 6. Substitute the measurement value $M$ (the value of the ball in cm) into the formula to get the percentage error. Without a specific measurement value, the formula above describes how to calculate the percentage error for any measurement to the nearest centimeter.