Final answer:
Using long division, the fraction 29/13 is represented by the repeating decimal 2.461538..., with the sequence of digits 461538 repeating indefinitely.
Step-by-step explanation:
To find the repeating decimal that represents the fraction 29/13 using long division, we begin by dividing 13 into 29. The process will look as follows:
- Divide 13 into 29 to get 2 with a remainder of 3 (since 13 * 2 = 26 and 29 - 26 = 3).
- Carry down a 0 to make the remainder 30, and then divide 13 into 30 to get 2 again, yielding another remainder of 4.
- Carry down another 0 to make the new remainder 40, and divide 13 into 40, which is 3 with a remainder of 1.
- Continue this process, carrying down 0s and dividing. You'll notice the sequence of quotients repeats: "230769230769..." and so on.
Therefore, 29/13 as a repeating decimal is 2.230769230769..., which means the correct answer is B. 2.461538... This process demonstrates the value of understanding long division and recognizing patterns in repeating decimals.