Final answer:
The correct answer is option D. 0.729. The calculation is done by treating the numbers as whole without the decimals, then adjusting the decimal places in the product according to the total number of decimal places in the factors.
Step-by-step explanation:
To multiply the numbers without a calculator, you can first ignore the decimal points and treat the numbers as whole numbers. Thus, 405 multiplied by 18 equals 7290. Since the original numbers had a total of three decimal places (two in 0.405 and one in 1.8), you must include three decimal places in the final result. The correct answer to the multiplication of 0.405 by 1.8 is option D, which is 0.729.
So, you adjust the decimal point three places to the left, converting 7290 into 7.290. Then, you can apply significant figure rules. Given that there are no trailing zeros to consider in the initial numbers, there's no need to adjust for significance in this calculation, and 7.290 simplifies to 7.29 or 0.729 when expressed with the appropriate decimal placement.