Sure, let's break this problem down step-by-step and find the solution together.
We need to determine the value of [tex]\(\left(9 \times 10^{-4}\right) \times \left(3 \times 10^7\right)\)[/tex] and express it in standard form.
1. Identify each term:
- The first term is [tex]\(9 \times 10^{-4}\)[/tex].
- The second term is [tex]\(3 \times 10^7\)[/tex].
2. Express each term in decimal form:
- [tex]\(9 \times 10^{-4} = 0.0009\)[/tex]
- [tex]\(3 \times 10^7 = 30,000,000\)[/tex]
3. Calculate the product of these decimal numbers:
[tex]\[
0.0009 \times 30,000,000
\][/tex]
4. Multiplying the decimal numbers:
[tex]\[
0.0009 \times 30,000,000 = 27,000
\][/tex]
5. Express the result [tex]\(27,000\)[/tex] in standard form:
Standard form is a way of writing numbers as a product of a coefficient and a power of 10. The coefficient must be a number between 1 and 10.
[tex]\(27,000\)[/tex] can be expressed as:
[tex]\[
27,000 = 2.7 \times 10^4
\][/tex]
Here, the coefficient is [tex]\(2.7\)[/tex] and the exponent is [tex]\(4\)[/tex].
So, the final answer to the problem [tex]\(\left(9 \times 10^{-4}\right) \times \left(3 \times 10^7\right)\)[/tex] in standard form is:
[tex]\[
2.7 \times 10^4
\][/tex]
