Final answer:
To sum 2.77 and 9 while maintaining significant figures, add the numbers to get 11.77 and then round to the hundredths place. No rounding is required since the sum is already precise to the hundredths place, resulting in a final answer of 11.77.
Step-by-step explanation:
When solving the problem of adding 2.77 and 9, we first perform the addition to get 11.77. However, to maintain the correct significant figures and round accordingly, we need to observe the least precise number in the operation. In this case, since 2.77 has significant figures up to the hundredths place, the final result also needs to be rounded to the hundredths place.
To round to the nearest thousandths, we check the digit in the thousandths place. If this digit is 5 or greater, we round the hundredths place up. Otherwise, we leave it as is. Since there is no digit in the thousandths place in our sum (11.77), we don't need to alter the hundredths place.
Therefore, the properly rounded answer to 2.77 + 9, considering significant figures, is 11.77.