To express the federal debt of country C, which is $278,560,125,000, in the form of a single digit times an integer power of 10, we can first look at the leading digits.
The number is approximately 2.78560125 × 10^11. However, for estimation purposes, we can round it to 2.8 × 10^11, which is close to 2.79 × 10^11.
Thus, the closest estimation of this amount in the given options is:
2.79 × 10^11