1. The problem is to multiply the numbers 645.275 and 37. 2. Multiply as if they were whole numbers: $645275 \times 37$. 3. Calculate the multiplication: $645275 \times 37 = 23835275$. 4. Since 645.275 has three decimal places, put the decimal point three places from the right in the product. 5. Final result: $23835.275$.