To calculate the product of \( 840 \) and \( 4.6 \times 10^2 \), we'll start by performing the multiplication step-by-step and then convert the result into scientific notation.
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Multiply \( 840 \) and \( 4.6 \):
\[ 840 \times 4.6 = 3876 \]
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Next, multiply by \( 10^2 \) (which is 100):
\[ 3876 \times 100 = 387600 \]
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Now, convert \( 387600 \) into scientific notation. To do this, we need to express it as a number between \( 1 \) and \( 10 \) multiplied by a power of \( 10 \):
\[ 387600 = 3.876 \times 10^5 \]
So the product of \( 840 \) and \( 4.6 \times 10^2 \) expressed in scientific notation is:
\[ \boxed{3.876 \times 10^5} \]
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