To determine which number best approximates the national debt as of January 20, 2008, we start with the given total national debt: $10,024,724,896,912.49.
### Step-by-step Process:
1. Expressing the National Debt in Scientific Notation:
- The total national debt is [tex]\( 10,024,724,896,912.49 \)[/tex].
- We need to express this large number in a more manageable form using scientific notation.
2. Identifying the Significant Figures:
- The leading significant figures of our number are 10.024.
- The remaining digits can be approximated as moving the decimal point to the appropriate place in scientific notation.
3. Determining the Power of 10:
- By moving the decimal point 12 places to the left, we get [tex]\(10.024\)[/tex] as the coefficient.
- Therefore, [tex]\(10,024,724,896,912.49 \approx 10.024 \times 10^{12}\)[/tex].
### Comparing Options:
- Option A: [tex]\(10.024 \times 10^9\)[/tex]
- This would only be [tex]\(10,024,000,000\)[/tex], which is much smaller than the actual debt.
- Option B: [tex]\(10.024 \times 10^{10}\)[/tex]
- This would only be [tex]\(100,240,000,000\)[/tex], which is still significantly smaller.
- Option C: [tex]\(10.024 \times 10^{12}\)[/tex]
- This matches our calculated approximation of [tex]\( 10,024,000,000,000 \approx \text{TOTAL Debt}\)[/tex].
- Option D: [tex]\(10.024 \times 10^{14}\)[/tex]
- This would be [tex]\(1,002,400,000,000,000\)[/tex], which is far larger than the actual debt.
### Conclusion:
Since the value [tex]\(10.024 \times 10^{12}\)[/tex] best approximates the national debt calculated:
The best approximation is option C.
