A factory produces 2.3 x 10^5 marbles per hour. How many marbles will be produced after 200 hours?

223 x 10^5 marbles
200 marbles
4.6 x 10^7 marbles
4.3 x 10^10 marbles

1 answer

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.