Question

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

Answer 1

To estimate the amount of the federal debt of Country C, we can express it in the form of a single digit times an integer power of 10.

The given federal debt is $278,560,125,000.

First, we can rewrite this amount in scientific notation. To convert this to scientific notation, we want a number between 1 and 10 multiplied by a power of 10:

1. Move the decimal point in 278,560,125,000 to the left until one digit remains to the left of the decimal point.

   • We move the decimal point 11 places to the left:
   • \(2.78560125\)

2. Now multiply it by \(10^{11}\) (since we moved the decimal 11 places).

Combining these steps, we have:

\[ 278,560,125,000 \approx 2.79 \times 10^{11} \]

Looking at the provided responses, the closest estimation is:

2.79 × 10²¹

So, the correct answer is: 2.79 × 10¹¹.