To simplify the expression [tex]\( \left(4 \times 10^6\right) \cdot 10^{-3} \)[/tex], follow these steps:
1. Understand the problem: We need to multiply the number [tex]\( 4 \times 10^6 \)[/tex] by [tex]\( 10^{-3} \)[/tex].
2. Multiply the coefficients: The base numbers (coefficients) can be multiplied directly. Here, the coefficient is 4.
3. Add the exponents: When multiplying numbers in scientific notation, add the exponents of the base 10 terms. Specifically, [tex]\(10^6\)[/tex] and [tex]\(10^{-3}\)[/tex]:
[tex]\[
10^6 \times 10^{-3} = 10^{6 + (-3)} = 10^{3}
\][/tex]
4. Combine the results: Now combine the coefficient with the simplified base 10 term:
[tex]\[
4 \times 10^6 \cdot 10^{-3} = 4 \times 10^3
\][/tex]
5. Express in scientific notation: The result can be directly written in scientific notation as:
[tex]\[
4.0 \times 10^3
\][/tex]
6. Verify and match the answer with provided options:
- A. [tex]\(4 \times 10^{-18}\)[/tex]
- B. [tex]\(4 \times 10^3\)[/tex]
- C. 4,000
- D. [tex]\(4 \times 10^9\)[/tex]
Since [tex]\(4.0 \times 10^3\)[/tex] is the same as [tex]\(4 \times 10^3\)[/tex], the correct option is:
[tex]\[
\boxed{B}
\][/tex]
Option B is the correct answer. Thus, [tex]\( \left(4 \times 10^6\right) \cdot 10^{-3} \)[/tex] simplifies to [tex]\( 4 \times 10^3 \)[/tex].
