To solve the problem [tex]\(\frac{6.0 \times 10^4}{4.0 \times 10^8}\)[/tex] and express the answer in proper scientific notation, follow these steps:
1. Separate the coefficients and the powers of ten:
[tex]\[
\frac{6.0}{4.0} \times \frac{10^4}{10^8}
\][/tex]
2. Simplify the coefficients:
[tex]\[
\frac{6.0}{4.0} = 1.5
\][/tex]
3. Simplify the powers of ten using the property of exponents [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[
\frac{10^4}{10^8} = 10^{4-8} = 10^{-4}
\][/tex]
4. Combine the simplified coefficient and the power of ten:
[tex]\[
1.5 \times 10^{-4}
\][/tex]
Therefore, the result of the operation [tex]\(\frac{6.0 \times 10^4}{4.0 \times 10^8}\)[/tex] in proper scientific notation is:
[tex]\[
1.5 \times 10^{-4}
\][/tex]
