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

Responses

3 × 1011
3 times 10 superscript 11 baseline

2.79 × 1011
2.79 times 10 superscript 11 baseline

2 × 1011
2 times 10 superscript 11 baseline

3 × 10−11
3 times 10 superscript negative 11 baseline

Answer 1

To express the federal debt of Country C, $278,560,125,000, in scientific notation, we want to approximate it in the form \( a \times 10^b \), where \( 1 \leq a < 10 \).

1. First, identify the significant figures in the number. The significant digits are 2.78560125.
2. To express this in scientific notation, we need to move the decimal point left until we have a single digit to the left of the decimal. Moving the decimal point 11 places to the left gives us: \[ 2.78560125 \times 10^{11} \]
3. Rounding this to two decimal places gives us \( 2.79 \times 10^{11} \).

Thus, the closest estimation of the federal debt of Country C is:

2.79 × 10^11