To find out how many neon tetras can be housed in the aquarium, we need to divide the total volume of the aquarium by the amount of water each neon tetra requires.
The total volume of the aquarium is given as \( 1 \times 10^5 \) gallons and each neon tetra needs \( 1.25 \) gallons.
We can calculate the number of tetras as follows:
\[ \text{Number of tetras} = \frac{\text{Total volume of aquarium}}{\text{Volume per tetra}} = \frac{1 \times 10^5 \text{ gallons}}{1.25 \text{ gallons}} \]
Now, calculating the division:
\[ \frac{1 \times 10^5}{1.25} \]
To simplify \( \frac{1}{1.25} \), we convert \( 1.25 \) to a fraction:
\[ 1.25 = \frac{5}{4} \]
Thus,
\[ \frac{1}{1.25} = \frac{1}{\frac{5}{4}} = \frac{4}{5} \]
Calculating \( \frac{1 \times 10^5}{1.25} \):
\[ \frac{1 \times 10^5}{1.25} = 4 \times 10^5 \div 5 = 0.8 \times 10^5 \]
Next, we convert \( 0.8 \times 10^5 \) to scientific notation:
\[ 0.8 \times 10^5 = 8 \times 10^{-1} \times 10^5 = 8 \times 10^{4} \]
Thus, the total number of neon tetras that the aquarium can house is
\[ \boxed{8 \times 10^4} \]