Let's solve the problem step-by-step.
1. Identify the given values:
- Numerator: [tex]\( 3.0 \times 10^4 \)[/tex]
- Denominator: [tex]\( 4.0 \times 10^8 \)[/tex]
2. Perform the division of these values:
[tex]\[
\frac{3.0 \times 10^4}{4.0 \times 10^8} = \frac{3.0}{4.0} \times \frac{10^4}{10^8}
\][/tex]
3. Simplify the numerical part:
[tex]\[
\frac{3.0}{4.0} = 0.75
\][/tex]
4. Simplify the power of ten part:
[tex]\[
\frac{10^4}{10^8} = 10^{4-8} = 10^{-4}
\][/tex]
5. Combine the simplified parts:
[tex]\[
0.75 \times 10^{-4}
\][/tex]
6. Convert the result to correct scientific notation:
- In scientific notation, the coefficient should be a value between 1 and 10.
- To convert [tex]\( 0.75 \times 10^{-4} \)[/tex] to the correct form, we can express [tex]\( 0.75 \)[/tex] as [tex]\( 7.5 \times 10^{-1} \)[/tex]:
[tex]\[
0.75 \times 10^{-4} = (7.5 \times 10^{-1}) \times 10^{-4}
\][/tex]
- Combine the powers of ten:
[tex]\[
7.5 \times 10^{-1-4} = 7.5 \times 10^{-5}
\][/tex]
Therefore, the answer in correct scientific notation is:
[tex]\[ 7.5 \times 10^{-5} \][/tex]
