To multiply numbers in scientific notation, you can follow these steps:
- Multiply the coefficients (the numbers in front).
- Add the exponents of the powers of 10.
Given the expression:
\[ (1.25 \times 10^5) \times (9.2 \times 10^2) \]
Step 1: Multiply the coefficients.
\[ 1.25 \times 9.2 = 11.5 \]
Step 2: Add the exponents.
\[ 10^5 \times 10^2 = 10^{(5 + 2)} = 10^7 \]
Step 3: Combine the results.
\[ 11.5 \times 10^7 \]
Since \(11.5\) is not between \(1\) and \(10\), we'll convert it into proper scientific notation:
\[ 11.5 = 1.15 \times 10^1 \]
Now, we add the exponents:
\[ 1.15 \times 10^1 \times 10^7 = 1.15 \times 10^{(1 + 7)} = 1.15 \times 10^8 \]
Therefore, the result in scientific notation is:
\[ \boxed{1.15 \times 10^8} \]