To express $278,560,125,000 in the form of a single digit times an integer power of 10, we need to identify the significant figures and the power of 10.
The number $278,560,125,000 can be expressed in scientific notation as follows:
- Identify the first significant digit, which is 2.
- Move the decimal point so that there's one non-zero digit to the left of the decimal. Thus, we have 2.78560125.
- Count how many places we moved the decimal to obtain this value. We moved it 11 places to the left.
So, we can express the number as:
\[ 2.78560125 \times 10^{11} \]
Now, keeping only one significant figure gives us:
\[ 2.8 \times 10^{11} \]
However, if we need to select the closest option from the provided responses and maintain just a single significant digit, we round it to:
\[ 2 \times 10^{11} \]
Thus, the closest estimation of the federal debt of Country C at the end of fiscal year 2004, expressed in the required form, is:
2 × 10^11