1. **State the problem:** Express 0.000407 correct to two significant figures. 2. **Understand significant figures:** Significant figures are digits that carry meaning contributing to its precision. For two significant figures, we keep the first two non-zero digits. 3. **Identify the first two significant figures:** In 0.000407, the first two significant digits are 4 and 0 (the zeros after the decimal but before the 4 are not significant). 4. **Round the number:** The third digit after the first two significant figures is 7, which is greater than 5, so we round the second significant figure up. 5. **Calculate:** $$0.000407 \approx 0.00041$$ 6. **Final answer:** The number 0.000407 expressed to two significant figures is **0.00041**.