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 if 10.

Answer 1

To estimate the federal debt of country C at the end of fiscal year 2004, we can express the number in scientific notation.

The given amount is \( 278,560,125,000 \).

First, we can rewrite that in a simpler form:

1. Identify the leading digit: The first digit is 2.
2. Count the total number of digits after the first digit: There are 11 digits total (counting from the 2).
3. To express this in scientific notation, we recognize that the number can be expressed as: \[ 2.78560125 \times 10^{11} \]

However, to provide an estimation, we can round \( 2.78560125 \) to \( 3 \) (the closest single digit).

Thus, the estimation becomes: \[ 3 \times 10^{11} \]

So, the closest estimation of the federal debt is: \[ 3 \times 10^{11} \]

Answer 2

how many times less is 10^2 then 10^6? express your answer as an integer power of 10

Answer 3

To find how many times less \(10^2\) is than \(10^6\), you can divide \(10^6\) by \(10^2\):

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

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

So, the answer is:

\[ 10^4 \]

Answer 4

roughly, it takes light less than 0.000000003 of second to travel a one-meter distance. express this number in the form of a x 10^6n where 1 < a < 10 is a one-digit number

Answer 5

To express \(0.000000003\) seconds in the form of \(a \times 10^{6n}\), where \(1 < a < 10\), we first convert the number to scientific notation.

Starting with the number: \[ 0.000000003 \]

We can express this in scientific notation:

1. Move the decimal point to the right until we have a number between 1 and 10. In this case, we move it 9 places to the right: \[ 3 \times 10^{-9} \]

Now, to express this in the specific form \(a \times 10^{6n}\):

• We need to relate \(10^{-9}\) to a base of \(10^{6n}\):
  • Rewrite \(10^{-9}\) as \(10^{-9} = 10^{6(-2) + 3} = 10^{6 \cdot -2} \times 10^3\).

Thus we can write: \[ 3 \times 10^{-9} = 3 \times 10^{3} \times 10^{-12} \]

Wherein this conversion we have:

• \(a = 3\)
• And the notated \(n = -2\).

Thus, the result is: \[ 3 \times 10^{-9} = 3 \times 10^{6(-2)} \approx 3 \times 10^{-9} \]

The final formatted version we wanted was previously : \[ 3 \times 10^{6(-2)} \]

However, to emphasize it clearly: The value:

So:

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

Which can also be written in the form \(a \times 10^{6n}\) as required.

Thus referring back to your original format \(( a = 3 )\), leads to the context above.

Please let me know if you require more clarification on any notation or steps!