Let's walk through the steps to solve the problem [tex]\(\frac{6.0 \times 10^2}{8.0 \times 10^{12}}\)[/tex] and express the answer in correct scientific notation.
1. Identify the given values:
- Numerator: [tex]\(6.0 \times 10^2\)[/tex]
- Denominator: [tex]\(8.0 \times 10^{12}\)[/tex]
2. Separate the constants from the powers of ten:
- Constants: [tex]\(6.0\)[/tex] and [tex]\(8.0\)[/tex]
- Powers of ten: [tex]\(10^2\)[/tex] and [tex]\(10^{12}\)[/tex]
3. Divide the constants:
[tex]\[
\frac{6.0}{8.0} = 0.75
\][/tex]
4. Subtract the exponents (since the bases are the same and we are dividing):
[tex]\[
10^2 \div 10^{12} = 10^{2 - 12} = 10^{-10}
\][/tex]
5. Combine the result of the constants with the result of the powers of ten:
[tex]\[
0.75 \times 10^{-10}
\][/tex]
6. Express [tex]\(0.75\)[/tex] in scientific notation:
[tex]\[
0.75 = 7.5 \times 10^{-1}
\][/tex]
7. Combine the two parts with correct exponent manipulation:
[tex]\[
(7.5 \times 10^{-1}) \times 10^{-10}
\][/tex]
8. Add the exponents:
[tex]\[
7.5 \times 10^{-1 + (-10)} = 7.5 \times 10^{-11}
\][/tex]
Therefore, the final result in scientific notation is [tex]\( \boxed{7.5 \times 10^{-11}} \)[/tex].
This means:
- The coefficient is [tex]\(7.5\)[/tex].
- The exponent is [tex]\(-11\)[/tex].
So, the detailed solution for the given operation [tex]\(\frac{6.0 \times 10^2}{8.0 \times 10^{12}}\)[/tex] results in [tex]\(7.5 \times 10^{-11}\)[/tex].
