10. Washing a pile of vegetables to remove residual pesticides with water. The effect of washing once with a certain amount of water is assumed as follows: 1 unit of water can remove $\frac{1}{2}$ of the residual pesticides on the vegetables. The more water used, the more pesticides are removed, but there will always be some pesticides left on the vegetables. Let the ratio of the residual pesticide amount on the vegetables after washing once with $x$ units of water to the residual pesticide amount before washing be the function $f(x)$.
(1) Specify the value of $f(0)$ and explain its practical significance;
(2) Write down the conditions and properties that the function $f(x)$ should satisfy based on the assumptions;
(3) Suppose $f(x)=\frac{1}{1+x^{2}}$. Given $a (a>0)$ units of water, you can wash once, or you can divide the water into 2 equal parts and wash twice. Which method leaves fewer residual pesticides on the vegetables? Explain your reasoning.
10. (1) $f(0)=1$ indicates that without washing, the amount of pesticide on the vegetables remains unchanged.
(2) The conditions and properties that $f(x)$ should satisfy are:
$f(0)=1, f(1)=\frac{1}{2}, f(x)$ is monotonically decreasing on $[0,+\infty)$, and $02 \sqrt{2}$, $f_{1}>f_{2}$, washing twice results in less residual pesticide; when $a=2 \sqrt{2}$, $f_{1}=f_{2}$, both washing methods have the same effect; when $0<a<2 \sqrt{2}$, $f_{1}<f_{2}$, washing once results in less residual pesticide.