Why can't I throw an exception from a method

I am new at Java and am experiencing a bit of a problem with throwing exceptions. Namely, why is this incorrect

public static void divide(double x, double y) {
    if (y == 0){
        throw new Exception("Cannot divide by zero."); 
        // Generates error message that states the exception type is unhanded 
    }
    else
        System.out.println(x + " divided by " + y + " is " + x/y);
        // other code follows
}

But this OK?

public static void divide(double x, double y) {
    if (y == 0)
        throw new ArithmeticException("Cannot divide by zero.");
    else
        System.out.println(x + " divided by " + y + " is " + x/y);
        // other code follows
}

An ArithmeticException is a RuntimeException, so it doesn't need to be declared in a throws clause or caught by a catch block. But Exception isn't a RuntimeException.

Section 11.2 of the JLS covers this:

The unchecked exception classes (§11.1.1) are exempted from compile-time checking.

The "unchecked exception classes" include Errors and RuntimeExceptions.

Additionally, you'll want to check if y is 0, not if x / y is 0.