Calculate the product below and give your answer in scientific notation.

To calculate the product \( (800) \times (3 \times 10^{-1}) \), we can first simplify \( 800 \) in terms of scientific notation.

The number \( 800 \) can be written as: \[ 800 = 8 \times 10^2 \] Now, we substitute this form into the expression: \[ (800) \times (3 \times 10^{-1}) = (8 \times 10^2) \times (3 \times 10^{-1}) \]

Next, we multiply the coefficients (8 and 3) together, and the powers of ten separately: \[ (8 \times 3) \times (10^2 \times 10^{-1}) = 24 \times 10^{2 - 1} = 24 \times 10^1 \]

Now, we convert \( 24 \times 10^1 \) into proper scientific notation. In scientific notation, we express \( 24 \) as \( 2.4 \times 10^1 \): \[ 24 \times 10^1 = 2.4 \times 10^{1 + 1} = 2.4 \times 10^2 \]

Hence, the final product in scientific notation is: \[ \boxed{2.4 \times 10^2} \]