To determine the correct scientific notation for the number [tex]\(724,000,000,000\)[/tex], let’s follow the steps:
1. Identify the Significant Figures:
- The number given is [tex]\(724,000,000,000\)[/tex]. The significant figures here are 724.
2. Writing the Number in Terms of a Power of 10:
- We need to express 724,000,000,000 in the form [tex]\(a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex].
3. Adjusting the Significant Figures:
- To convert 724,000,000,000 to a number between 1 and 10, we move the decimal point 11 places to the left.
- So, [tex]\(724,000,000,000\)[/tex] becomes [tex]\(7.24\)[/tex].
4. Determining the Exponential Part:
- Since we moved the decimal point 11 places to the left, the exponent [tex]\(b\)[/tex] is 11.
5. Combining Both Parts:
- Therefore, [tex]\(724,000,000,000\)[/tex] can be written as [tex]\(7.24 \times 10^{11}\)[/tex] in scientific notation.
Given the options:
- A. [tex]\(7.24 \times 10^{11}\)[/tex]
- B. [tex]\(72.4 \times 10^{11}\)[/tex]
- C. [tex]\(7.24 \times 10^{10}\)[/tex]
- D. [tex]\(724 \times 10^9\)[/tex]
Option A correctly matches our scientific notation of [tex]\(7.24 \times 10^{11}\)[/tex].
So, the correct answer is:
A. [tex]\(7.24 \times 10^{11}\)[/tex].
