1. **State the problem:** Calculate $$(4.15 \times 10^{-3}) - (3.64 \times 10^{-3})$$ and write the answer in scientific notation. 2. **Recall the rule:** When subtracting numbers in scientific notation with the same power of ten, subtract the coefficients and keep the power of ten the same. 3. **Perform the subtraction:** $$4.15 \times 10^{-3} - 3.64 \times 10^{-3} = (4.15 - 3.64) \times 10^{-3}$$ 4. **Calculate the difference of coefficients:** $$4.15 - 3.64 = 0.51$$ 5. **Write the intermediate result:** $$0.51 \times 10^{-3}$$ 6. **Convert to proper scientific notation:** Since $0.51$ is not between 1 and 10, rewrite as: $$0.51 \times 10^{-3} = 5.1 \times 10^{-1} \times 10^{-3} = 5.1 \times 10^{-4}$$ 7. **Final answer:** $$\boxed{5.1 \times 10^{-4}}$$ This is the correct scientific notation for the subtraction result.