To multiply the given numbers in scientific notation, follow these steps:
Given:
- \( 4.82 \times 10^{12} \)
- \( 3.2 \times 10^{4} \)
Step 1: Multiply the coefficients
Multiply the two decimal numbers: \[ 4.82 \times 3.2 \]
Calculating: \[ 4.82 \times 3.2 = 15.424 \]
Step 2: Add the exponents
Add the exponents of 10: \[ 10^{12} \times 10^{4} = 10^{(12 + 4)} = 10^{16} \]
Step 3: Combine the results
Now combine the results from Step 1 and Step 2: \[ 15.424 \times 10^{16} \]
Step 4: Adjust the coefficient if necessary
Since the coefficient \( 15.424 \) is greater than 10, we need to convert it to scientific notation: \[ 15.424 = 1.5424 \times 10^{1} \]
So: \[ 15.424 \times 10^{16} = 1.5424 \times 10^{1} \times 10^{16} = 1.5424 \times 10^{(1 + 16)} = 1.5424 \times 10^{17} \]
Final Answer
Thus, the final answer for the multiplication of the two numbers is: \[ 4.82 \times 10^{12} \times 3.2 \times 10^{4} = 1.5424 \times 10^{17} \]