Final answer:
To round 491 x 10.71 to the greatest place value, multiply 491 by 10.71 to get 5,264.61. Round the answer to the hundredths place because of the significant figures in 10.71, resulting in 5,264.62.
Step-by-step explanation:
To round 491 x 10.71 to the greatest place value, we can first perform the multiplication: 491 x 10.71 = 5,264.61. Since the farthest-right significant figure in 10.71 is in the hundredths place, we need to round the final answer to the hundredths place. The digit to the right of the hundredths place is 6, which is greater than 5, so we round up. Therefore, the rounded answer is 5,264.62.