1. **State the problem:** Multiply the numbers 5.732 and 222. 2. **Recall the multiplication rule:** To multiply decimals, multiply as if they were whole numbers, then place the decimal point in the product. 3. **Multiply 5732 by 222:** $$5732 \times 222 = 1271904$$ 4. **Adjust for decimals:** Since 5.732 has three decimal places, the product should have three decimal places. 5. **Place the decimal point:** $$1271.904$$ 6. **Final answer:** $$5.732 \times 222 = 1271.904$$