Question

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) Responses 3 × 10−11 3 times 10 superscript negative 11 baseline 2.79 × 1011 2.79 times 10 superscript 11 baseline 3 × 1011 3 times 10 superscript 11 baseline 2 × 1011 2 times 10 superscript 11 baseline

Answer 1

To express the federal debt of Country C, $278,560,125,000, in the form of a single digit times an integer power of 10, we can rewrite the number in scientific notation.

The number $278,560,125,000 can be approximated as follows:

1. Identify the first significant digit: 2.
2. Move the decimal point to the right until only one digit is to the left of the decimal: 2.78560125.
3. Count how many places you moved the decimal: from the end of the number (11 places to the left).
4. Thus, the expression in scientific notation becomes \( 2.78560125 \times 10^{11} \).

Since we need to express it in a single digit times an integer power of 10 and find the closest estimation, we round \( 2.78560125 \) to \( 2.79 \).

Hence, the closest approximation is: \[ 2.79 \times 10^{11} \]

Therefore, the final answer is: \[ \text{2.79 × 10}^{11} \]