1. **Stating the problem:** Calculate the product of $1.005$ and $96$. 2. **Formula used:** Multiplication of two numbers: $$a \times b$$ 3. **Intermediate work:** $$1.005 \times 96 = 1.005 \times (100 - 4) = 1.005 \times 100 - 1.005 \times 4$$ 4. **Calculate each term:** $$1.005 \times 100 = 100.5$$ $$1.005 \times 4 = 4.02$$ 5. **Subtract:** $$100.5 - 4.02 = 96.48$$ 6. **Final answer:** $$\boxed{96.48}$$