To write [tex]\(\frac{97}{11}\)[/tex] as a decimal, we need to perform the division of 97 by 11.
1. Divide 97 by 11. When we carry out the division, the quotient (the result of the division) will be approximately 8.818181818181818.
Next, let's match this result with the given options to find the correct answer.
- 8.818: This option is a truncated version of our result and doesn't fully capture the repeating nature of the decimal.
- [tex]\(8 . \overline{81}\)[/tex]: This option suggests that 81 repeats indefinitely, which is not the case.
- [tex]\(8.81 \overline{8}\)[/tex]: This is the correct representation since 8 repeats indefinitely after 8.81.
- [tex]\(8.8 \overline{1}\)[/tex]: This suggests that 1 repeats after 8.8, which is not accurate.
Therefore, the correct answer is [tex]\(8.81 \overline{8}\)[/tex].
