Question

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

Answer 1

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.