1. **State the problem:** Josie scored 1276 points in Round 1 and 1234 points in Round 2. We need to find the percentage decrease in her score. 2. **Formula for percentage decrease:** $$\text{Percentage Decrease} = \frac{\text{Original Score} - \text{New Score}}{\text{Original Score}} \times 100$$ 3. **Substitute the values:** $$\frac{1276 - 1234}{1276} \times 100$$ 4. **Calculate the difference:** $$\frac{42}{1276} \times 100$$ 5. **Simplify the fraction:** $$\frac{\cancel{42}}{\cancel{1276}} \times 100$$ (no common factors to cancel here, so fraction remains as is) 6. **Divide and multiply:** $$\approx 0.03292 \times 100 = 3.292\%$$ 7. **Check the calculation:** The handwritten answer says 16%, but the calculation above shows about 3.29%. Let's re-examine the subtraction: $$1276 - 1234 = 42$$ which is correct. 8. **Recalculate percentage decrease:** $$\frac{42}{1276} \times 100 \approx 3.29\%$$ 9. **Conclusion:** The percentage decrease is approximately **3.29%**, not 16%. The 16% in the handwritten note seems to be an error. **Final answer:** $$\boxed{3.29\%}$$