To find out how many marbles are produced after 200 hours, we can multiply the production rate by the number of hours.
Given:
- Production rate = \( 2.3 \times 10^5 \) marbles per hour
- Time = 200 hours
The total production can be calculated as follows:
\[ \text{Total Production} = \text{Production rate} \times \text{Time} \] \[ \text{Total Production} = (2.3 \times 10^5) \times 200 \]
First, convert 200 into scientific notation:
\[ 200 = 2.0 \times 10^2 \]
Now, substitute this back into the equation:
\[ \text{Total Production} = (2.3 \times 10^5) \times (2.0 \times 10^2) \]
When multiplying in scientific notation, you can multiply the coefficients and add the exponents:
\[ \text{Total Production} = (2.3 \times 2.0) \times (10^5 \times 10^2) \] \[ \text{Total Production} = 4.6 \times 10^{5 + 2} \] \[ \text{Total Production} = 4.6 \times 10^7 \]
Thus, the number of marbles produced after 200 hours is:
\[ \boxed{4.6 \times 10^7} \text{ marbles} \]
This matches with one of the options provided.