Alright, let's solve the following problem step-by-step:
We start with the given fraction:
[tex]\[ \frac{3.0 \times 10^4}{4.0 \times 10^8} \][/tex]
1. Divide the coefficients:
[tex]\[ \frac{3.0}{4.0} = 0.75 \][/tex]
2. Subtract the exponents of 10 (since [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]):
[tex]\[ 10^4 = 10^{4-8} = 10^{-4} \][/tex]
3. Combine the results:
[tex]\[ \frac{3.0 \times 10^4}{4.0 \times 10^8} = 0.75 \times 10^{-4} \][/tex]
Now, we need to express this result in proper scientific notation. Recall that in scientific notation, the coefficient must be a value between 1 and 10. Therefore, we need to convert [tex]\(0.75 \times 10^{-4}\)[/tex] to a suitable form.
4. Convert the coefficient to be between 1 and 10:
[tex]\[ 0.75 = 7.5 \times 10^{-1} \][/tex]
5. Adjust the exponent accordingly:
[tex]\[ 0.75 \times 10^{-4} = (7.5 \times 10^{-1}) \times 10^{-4} = 7.5 \times 10^{-1-4} = 7.5 \times 10^{-5} \][/tex]
Hence, the answer in correct scientific notation is:
[tex]\[ \boxed{7.5 \times 10^{-5}} \][/tex]
So from the provided options:
- [tex]\(7.5 \times 10^{-4}\)[/tex]
- [tex]\(7.5 \times 10^{-5}\)[/tex]
- [tex]\(7.5 \times 10^{11}\)[/tex]
- [tex]\(0.75 \times 10^{-4}\)[/tex]
The correct answer is:
[tex]\[ 7.5 \times 10^{-5} \][/tex] which corresponds to the second option.
