4.82 X 10^12 x 3.2 X 10^4

Question

Multiply the numbers above. Show your work below.
X
For example: 2.3 X 10^3 + 1.7 × 10^3 = 4 × 10^3

Answer 1

To multiply the numbers \( 4.82 \times 10^{12} \) and \( 3.2 \times 10^{4} \), you can follow these steps:

1. Multiply the coefficients: \[ 4.82 \times 3.2 \]

   Calculating that: \[ 4.82 \times 3.2 = 15.424 \]

2. Add the exponents: When you multiply numbers in scientific notation, you add the exponents. So, you have \( 10^{12} \) and \( 10^{4} \): \[ 10^{12} \times 10^{4} = 10^{(12 + 4)} = 10^{16} \]

3. Combine the results: Putting these results together, you have: \[ 15.424 \times 10^{16} \]

4. Adjust to proper scientific notation: Since \( 15.424 \) is greater than \( 10 \), we should convert it into proper scientific notation. We can write \( 15.424 \) as \( 1.5424 \times 10^1 \).

   Thus, \[ 15.424 \times 10^{16} = 1.5424 \times 10^1 \times 10^{16} = 1.5424 \times 10^{(1 + 16)} = 1.5424 \times 10^{17} \]

So, the final product of \( 4.82 \times 10^{12} \) and \( 3.2 \times 10^{4} \) is: \[ \boxed{1.5424 \times 10^{17}} \]