To multiply the two numbers in scientific notation, you can follow these steps:
- Multiply the coefficients: \( 8.03 \times 4.82 \)
- Add the exponents: \( 10^{-8} \times 10^{12} \)
Let's calculate it step by step:
-
Coefficients: \[ 8.03 \times 4.82 \approx 38.6856 \]
-
Exponents: \[ 10^{-8} \times 10^{12} = 10^{-8 + 12} = 10^{4} \]
Now combine the results: \[ 38.6856 \times 10^{4} \]
In proper scientific notation, you want the coefficient to be between 1 and 10. So, we can rewrite \( 38.6856 \) as \( 3.86856 \times 10^{1} \). Thus, we have: \[ 3.86856 \times 10^{1} \times 10^{4} = 3.86856 \times 10^{5} \]
Therefore, the final result is approximately: \[ 3.87 \times 10^{5} \quad (\text{rounded to three significant figures}) \]