1. The problem is to multiply 641.1 by 8.9. 2. The multiplication formula is $a \times b = c$, where $a=641.1$ and $b=8.9$. 3. Multiply the numbers directly: $$641.1 \times 8.9$$ 4. Calculate step-by-step: $$641.1 \times 8.9 = 641.1 \times (8 + 0.9) = 641.1 \times 8 + 641.1 \times 0.9$$ 5. Calculate each part: $$641.1 \times 8 = 5128.8$$ and $$641.1 \times 0.9 = 576.99$$ 6. Add the results: $$5128.8 + 576.99 = 5705.79$$ 7. Therefore, the final answer is $5705.79$.