Final answer:
To find the decimal equivalent of 9/11, divide 9 by 11 using long division, which results in the repeating decimal 0.8181... where '81' repeats indefinitely.
Step-by-step explanation:
The student asked how to find the decimal equivalent of the fraction 9/11 using long division. To do this, we divide 9 by 11. First, we observe that 9 goes into 11 zero times, so we place a decimal point in the answer and bring down a zero, making the dividend 90. Eleven goes into 90 eight times (since 11 x 8 = 88), so eight is the next digit in the answer. Subtracting 88 from 90, we get a remainder of 2. Bringing down another zero, we now have 20. Eleven goes into 20 one time, and we have a remainder of 9. When we bring down another zero, we're back to 90, and the pattern will repeat, indicating that the decimal is repeating. The decimal equivalent of 9/11, therefore, is 0.8181..., where '81' is a repeating sequence.