1. **State the problem:** We are given two measurements $a = 40.10m$ and $b = 36.00m$. We need to find the percentage error in the quotient $\frac{a}{b}$. 2. **Formula for percentage error in quotient:** When dividing two quantities, the percentage error in the quotient is approximately the sum of the percentage errors of the numerator and denominator: $$\text{Percentage error in } \frac{a}{b} = \text{Percentage error in } a + \text{Percentage error in } b$$ 3. **Calculate percentage errors of $a$ and $b$:** Assuming the least count or uncertainty is the last digit given, the absolute errors are: - For $a = 40.10m$, absolute error $\Delta a = 0.01m$ - For $b = 36.00m$, absolute error $\Delta b = 0.01m$ Calculate percentage errors: $$\text{Percentage error in } a = \frac{\Delta a}{a} \times 100 = \frac{0.01}{40.10} \times 100 \approx 0.0249\%$$ $$\text{Percentage error in } b = \frac{\Delta b}{b} \times 100 = \frac{0.01}{36.00} \times 100 \approx 0.0278\%$$ 4. **Calculate total percentage error in quotient:** $$\text{Percentage error in } \frac{a}{b} = 0.0249\% + 0.0278\% = 0.0527\%$$ 5. **Final answer:** The percentage error in the quotient $\frac{a}{b}$ is approximately **0.053\%**.