Okay, here is a simple script:
Start()
{
Debug.Log((1f / 0).ToString());
}
And here is what this script gives in console:
Infinity
UnityEngine.Debug:Log(Object)
WTF??? It’s not a mathematical limit, guys. It suppose to give me an error! It’s not. It gives Infinity 
C# float type can represent infinity. Try it with integers and I’m sure you’ll get a different result 
What the end game here?
Dividing by zero doesn’t make any sense in the modern agreed upon maths, some argue here some argue there, what do you want this to mean?
In c# there are special cases for floats - NaN, Infinity, NegativeInfinity. It do not throws an exception because those values exists and they are legit. You should not expect errors not here, not anywhere. Relying on exceptions in your program logic is considered bad practice and it won’t give you anything except a headache. If you expect some error to happen, do not wait until it really happens. Check preconditions before running dangerous operation and change your execution flow in advance. In this case this means you should either check divider for being zero or check the result for being infinity, but do not wait for exception and do not change normal program flow from exception handling code.
Whats the point in dividing by zero exactly? I fail to see why this would ever be useful, except as a really weird way to clear out a value (which isnt really useful, just a use)
I can’t think of regular example of dividing by zero. Hardly remember if i ever did this. May be it can be used in shaders to get infinite white area where some parameter is zero instead of using ifs? This will give a little speed up maybe. I can assume the OP wants a error to happen when something what should not be 0 is actually 0. But it is much better to check in advance instead of waiting for an exception to happen