The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?

Analysis

To solve this problem, we need to calculate the percentage error. Percentage error is a measure of how far off a measurement is from the true or actual value, expressed as a percentage.

Concept

The formula for percentage error is:

• Measured Value: The value obtained during the measurement (0.21g).
• Actual Value: The true or correct weight (0.18g).
• Error: The difference between the measured and actual values.

Step-by-Step Solution

1. Find the absolute error: $$\text{Error} = \text{Measured Value} - \text{Actual Value}$$ $$\text{Error} = 0.21\text{g} - 0.18\text{g} = 0.03\text{g}$$

2. Calculate the percentage error: $$\text{Percentage Error} = \left( \frac{0.03}{0.18} \right) \times 100\%$$

3. Simplify the fraction: $$\frac{0.03}{0.18} = \frac{3}{18} = \frac{1}{6}$$

4. Convert to percentage: $$\frac{1}{6} \times 100\% = 16.666...\%$$

Rounding this to one decimal place gives 16.7%.

Conclusion

Comparing our result to the given options, 16.7% matches option D.

Exam Tip

When calculating percentage error, always remember that the denominator is the Actual Value (the "true" value), not the measured value. A common mistake students make is dividing by the measured value (0.21), which would lead to the wrong answer. Always keep the "True" value at the bottom!