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

Answer 1

To express the federal debt amount of Country C, which is $278,560,125,000, in the form of a single digit times an integer power of 10, we start by determining the proper form.

The number can be simplified as follows:

1. Identify where the decimal point needs to be placed to have only one non-zero digit before it. In this case, we move the decimal point in 278,560,125,000 to after the '2', resulting in 2.78560125.
2. Now we express the number as \(2.78560125 \times 10^{11}\), since moving the decimal point 11 places to the left gives us that value.

Next, we need an estimation, which typically rounds to a more manageable form. The number 2.78560125 can be rounded to 2.79 for this estimation.

Thus, the closest estimation of the federal debt amount in the required scientific notation format is:

2.79 × 10^11

So the correct response is:

2.79 × 10^11.