To find out how much water David would have to use per square foot of his garden, we can divide the total gallons of water he has by the area of the garden in square feet.
David has 412 gallons of water and his garden is 37 square feet in size.
We can calculate the amount of water per square foot using the formula:
\[ \text{Water per square foot} = \frac{\text{Total gallons}}{\text{Total square feet}} = \frac{412 \text{ gallons}}{37 \text{ square feet}} \]
Now, performing the division:
\[ \frac{412}{37} \approx 11.135135135135135 \]
Rounding this to the nearest tenth, we get:
\[ 11.1 \]
Thus, David would have to evenly distribute approximately 11.1 gallons of water for each square foot of his garden.