(1) A fish tank is a right rectangular prism that is $10 \frac{1}{2} \mathrm{in}$. long, $10 \mathrm{in}$. wide, and $12 \frac{1}{3}$ in. tall. How many cubic inches of water are needed to fill the tank?

Step 1 ：Given a fish tank that is a right rectangular prism with length = 10.5 in, width = 10 in, and height = 12.33 in.

Step 2 ：The volume of a rectangular prism is given by the formula \(\text{length} \times \text{width} \times \text{height}\).

Step 3 ：Substitute the given values into the formula: \(\text{volume} = 10.5 \times 10 \times 12.33\).

Step 4 ：Calculate the volume to get \(\text{volume} = 1294.65\) cubic inches.

Step 5 ：Final Answer: The volume of the fish tank is \(\boxed{1294.65}\) cubic inches.