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

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

2 × 1011
2 times 10 superscript 11 baseline

2.79 × 1011

Answer 1

How many times less is 102 than 106 ? Express your answer as an integer power of 10.(1 point)
Responses

10−4
10 superscript negative 4 baseline

10,000
10,000

0.0001
0.0001

104

Answer 2

Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of a × 10n where 1 < a < 10 and is a one-digit number.(1 point)
Responses

3 × 109
3 times 10 superscript 9 baseline

3 × 10−9
3 times 10 superscript negative 9 baseline

3 × 108
3 times 10 superscript 8 baseline

3 × 10−8

Answer 3

To express the federal debt of Country C, which is $278,560,125,000, in the form of a single digit times an integer power of 10, we look for a way to write this number in scientific notation.

The number is approximately 2.78560125 × 10^11. When rounding to one significant figure, it simplifies to approximately 3 × 10^11.

Therefore, the closest estimation of this amount is:

**3 × 10^11**.

Answer 4

To determine how many times less \(10^2\) is than \(10^6\), we divide \(10^6\) by \(10^2\):

\[
\frac{10^6}{10^2} = 10^{6-2} = 10^4
\]

This shows that \(10^2\) is \(10^4\) times less than \(10^6\).

Therefore, the answer is:

**10^4**.

Answer 5

To express the number \(0.000000003\) in the form \(a \times 10^n\), we can rewrite it in scientific notation.

The number \(0.000000003\) can be rewritten as:

\[
3 \times 10^{-9}
\]

Here, \(a = 3\) (which is between 1 and 10) and \(n = -9\).

Therefore, the correct expression of the number is:

**3 × 10^−9**.