At the end of fiscal year 2004, the federal debt of Country C is $278,560,125,000. What is the closest estimation of this amount? Express your answer in the form of a single digit times an integer power of 10.(1 point)

Question

3 × 10^−11

3 × 10^11

2 × 10^11

2.79 × 10^11

Answer 1

To estimate the federal debt of Country C, which is $278,560,125,000, we will express this amount in scientific notation.

1. Identify the leading digit: The leading digit is 2.
2. Count how many places we move the decimal point to the left to get it after the leading digit (2).
   • The original number is 278,560,125,000. Moving the decimal point 11 places to the left gives us 2.78560125.
3. Round to two significant figures: This rounds to 2.8 for simplicity.
4. Therefore, we put it in the scientific notation form:
   • \(2.78560125 \approx 2.8\) becomes \(2.8 \times 10^{11}\).
5. Although \(2.79 \times 10^{11}\) is close, \(2.8 \times 10^{11}\) would also be acceptable based on rounding conventions.

But given your options, the closest estimation of the federal debt in the requested form is:

2.79 × 10^11.