To find the cost to rent a video game for one day, you need to divide the total cost by the number of days. So the correct option is:
The cost to rent for one day is the quotient of $10 and 3.
This can be calculated as:
\[ \text{Cost for one day} = \frac{10}{3} \approx 3.33 \]
So the cost to rent the video game for one day is approximately $3.33.