1. **State the problem:** We need to find the relative percentage error of $x - y$ when $x$ and $y$ are chopped to five decimal digits. 2. **Given values:** - $x = 0.5725734781$ chopped to five decimals: $x_c = 0.57257$ - $y = 0.2716517285$ chopped to five decimals: $y_c = 0.27165$ 3. **Calculate the exact difference:** $$d = x - y = 0.5725734781 - 0.2716517285 = 0.3009217496$$ 4. **Calculate the chopped difference:** $$d_c = x_c - y_c = 0.57257 - 0.27165 = 0.30092$$ 5. **Calculate the absolute error:** $$|d - d_c| = |0.3009217496 - 0.30092| = 0.0000017496$$ 6. **Calculate the relative error:** $$\text{Relative error} = \frac{|d - d_c|}{|d|} = \frac{0.0000017496}{0.3009217496} \approx 5.81413 \times 10^{-6}$$ 7. **Convert to percentage:** $$\text{Relative percentage error} = 5.81413 \times 10^{-6} \times 100\% = 5.81413 \times 10^{-4}\%$$ **Final answer:** The relative percentage error is $5.81413 \times 10^{-4}\%$, which corresponds to option iii.