Purpose of throws clause in exception handling

Question

hi all,
I have written a sample code for exception handling...please refer below....
class a
void fun() throws ArithmeticException
int i=0;
i=10/0;
class exec
public static void main(String a[])
a a1=new a();
     try{a1.fun();}
     catch(ArithmeticException e){System.out.println("hi");}
}

Answer 1

I read the article...and came out with these points...
1..If method is throwing an unchecked exception (as in this case) then there is no need for throws clause, if you are not catching it then and there only.....
2...if a method is throwing a checked exception then either you need to catch it then and there only or you must specify a throws clause for the same in function definition......*And the purpose of not catching it then and there only is*
"For example, if you were providing the ListOfNumbers class as part of a package of classes, you probably couldn't anticipate the needs of all the users of your package. In this case, it's better to not catch the exception and to allow a method further up the call stack to handle it."
M I RIGHT??