Program to Display the Number of Digits in an integer

Problem: Write a method countDigits(n) that returns the number of digits in the integer 'n', which you may assume is positive. Design a main program to test your method. For hints about how to write this program, you might want to look back at the DigitSum program in Fig 4.6.

What I did: This program interacts with the user, taking in the digit input and sending that input to the countDigits method. I also made the program let the user keep entering in digits to his or her hearts' content, using the value "0" as the sentinel.

/*
/*
* File: DigitCountWithMethod.java
* Name: Chu
* Section Leader: 
* Description: This exercise prints the number of digits in an integer that
* the user enters in. The main/run method uses the digitCount method to 
* accomplish this.
* 
* The countDigits method is pretty clever and reuses the technique from the DigitSum program
* in the textbook from section 4.6. In order to count the number of digits in an 
* integer, you keep dividing the integer by 10 and adding 1 to a variable "dcount" that gets initiated
* at 0. You keep doing this iteration until the integer is zero.
*/


package ch6_practice;
import acm.program.*;

public class DigitCountWithMethod extends ConsoleProgram {
 
    public void run() {
        println("This program counts the digits in an integer.");
        //Hm, get "illegal numeric format" if it's a long integer...Java limitation? Eew.
  
        while (true) {
            int n = readInt ("Enter any integer, entering '0' if you want to exit the program:");
            if (n == 0) {
                println("Goodbye");
                break; //Oh, once you break, you can't continue in the loop; otherwise it's "unreachable code"       
            }
            else {
            println("There are " + countDigits(n) + " integers in " + n + ".");
            }
        }
    }
 
    private int countDigits(int n){
        int dcount = 0;
        while (n > 0) {
            dcount += 1;
            n /= 10;
        }
        return dcount;
    }
 
 
 
}

What made it tough: Nothing much; a lot of the countDigits strategy came from another program, DigitSum. I do see 2 curious things however. First; if the user enters in more than 10 digits, we get an error message "Illegal numeric format." Why??

Also, I wanted to let my program loop so that the user could enter in multiple digits; the only way I could think of how to do this was with establishing a sentinel with the value "0." However, this is not elegant at all; for one thing, what if I want to know how many digits zero has? However, I can't make the sentinel a string, since my prompt will only accept integers. Ideas on a better way for the user to terminate the program?