To determine how many light bulbs the company will produce in [tex]\(9.36 \times 10^2\)[/tex] weeks, given that they produce [tex]\(4.56 \times 10^3\)[/tex] light bulbs each week, we'll follow these steps:
1. Identify the weekly production and the number of weeks:
- Weekly production: [tex]\(4.56 \times 10^3\)[/tex] light bulbs
- Number of weeks: [tex]\(9.36 \times 10^2\)[/tex]
2. Multiply the weekly production by the number of weeks to find the total production:
- [tex]\(4.56 \times 10^3 \times 9.36 \times 10^2\)[/tex]
3. Multiply the coefficients (numbers in front of the powers of 10):
- [tex]\(4.56 \times 9.36\)[/tex]
4. Multiply the powers of 10:
- [tex]\(10^3 \times 10^2 = 10^{3+2} = 10^5\)[/tex]
5. Combine the results from the steps above:
- Calculate [tex]\(4.56 \times 9.36\)[/tex], which results in:
[tex]\[
4.56 \times 9.36 = 42.6816
\][/tex]
6. Express the result in scientific notation:
- [tex]\(42.6816 \times 10^5\)[/tex]
- This can be rewritten as [tex]\(4.26816 \times 10^6\)[/tex]
So, the total number of light bulbs produced is approximately [tex]\(4.26816 \times 10^6\)[/tex]. Comparing this result to the provided options, the best estimate is:
- [tex]\(4.5 \times 10^6\)[/tex] light bulbs
Thus, the correct answer is [tex]\(4.5 \times 10^6\)[/tex] light bulbs.
