1. **State the problem:** Express 0.0000407 correct to two significant figures. 2. **Understand significant figures:** Significant figures are the digits in a number that carry meaning contributing to its precision. To express a number to two significant figures means to keep only the first two non-zero digits and round accordingly. 3. **Identify the first two significant figures:** The number 0.0000407 can be written as $4.07 \times 10^{-5}$. 4. **Round to two significant figures:** The first two significant figures are 4 and 0. The third digit is 7, which is greater than 5, so we round the second digit up. 5. **Result after rounding:** $4.07 \times 10^{-5}$ rounded to two significant figures is $4.1 \times 10^{-5}$. 6. **Convert back to decimal form:** $4.1 \times 10^{-5} = 0.000041$. **Final answer:** 0.000041