To find out how many neon tetras can fit in the aquarium, we will divide the total gallons of water by the amount of water needed for each tetra.
- The total amount of water in the aquarium is \(1 \times 10^5\) gallons.
- Each neon tetra needs \(1.25\) gallons of water.
Now, we perform the division:
\[ \text{Number of tetras} = \frac{1 \times 10^5 \text{ gallons}}{1.25 \text{ gallons per tetra}} \]
To make the division easier, we can rewrite \(1.25\) in decimal form:
\[ 1.25 = \frac{125}{100} = \frac{5}{4} \]
Thus, the division becomes:
\[ \text{Number of tetras} = \frac{1 \times 10^5}{1.25} = \frac{1 \times 10^5}{\frac{5}{4}} = 1 \times 10^5 \times \frac{4}{5} \]
Calculating this step-by-step:
\[ 1 \times 10^5 \times \frac{4}{5} = \frac{4 \times 10^5}{5} \]
Now, we can perform the division \(4 \div 5\):
\[ = 0.8 \times 10^5 \]
To express \(0.8\) in scientific notation, we can rewrite it as:
\[ 0.8 = 8 \times 10^{-1} \]
Thus, we multiply:
\[ 0.8 \times 10^5 = 8 \times 10^{-1} \times 10^5 = 8 \times 10^{4} \]
So, the number of neon tetras that can fit in the aquarium is:
\[ \boxed{8 \times 10^4} \]