1. The problem asks for the 104th digit after the decimal point of the fraction $S = \frac{2222}{7777}$. 2. To find digits after the decimal point of a fraction, we perform long division of numerator by denominator. 3. Note that $7777 = 7 \times 1111$, and $2222 = 2 \times 1111$, so $S = \frac{2 \times 1111}{7 \times 1111} = \frac{2}{7}$. 4. The decimal expansion of $\frac{2}{7}$ is a repeating decimal with period 6: $0.285714285714...$ 5. The repeating block is "285714" which repeats indefinitely. 6. To find the 104th digit after the decimal, find the position within the repeating block: $$104 \mod 6 = 2$$ 7. The remainder 2 means the 104th digit corresponds to the 2nd digit in the repeating block. 8. The repeating block digits indexed: 1=2, 2=8, 3=5, 4=7, 5=1, 6=4. 9. Therefore, the 104th digit after the decimal point is $8$. Final answer: $8$