DecimalFormat not returning the right number

Question

Here's the prompt for this particular assignment: Let x be any real number. Write a program which calculates the square root of x by using Bisection method ( https://docs.python.org/3/library/functions.html#format ). Note that you should reduce this problem to the bisection method with a natural choice for a and b (ie, the user does not need to provide a and b). Note that Math.pow and Math.sqrt are not allowed.

The problem is that I'm not getting the right answers when I input whole numbers like 100 (which the root of is "10.0" but instead the console returns "9.999997615814209") or 36 ("6.0" but the console returns "5.999997138977051"). I think it may have to do with the fact I'm rounding the numbers or just the fact that I'm using doubles in general but I don't really understand mathematics in programming well. Thanks for helping me.

import java.text.DecimalFormat;
import java.util.Scanner;

public class BisectionMethod {

    public double a = 0;
    public double b;
    public double userInput;
    public int iteration = 0;
    public double midpoint;

    public static void main(String[] args) {
        BisectionMethod testClass = new BisectionMethod();
        System.out.println("Answer: " + testClass.FindAnswer(testClass.FindInput(), testClass.a, testClass.FindInterval()));
    }

    public double FindInput() {
        Scanner sc = new Scanner(System.in);
        System.out.println("Enter the number to find the root for: ");
        userInput = sc.nextDouble();
        while (userInput < 0) {
            System.out.println("Please enter a number bigger than 0: ");
            userInput = sc.nextDouble();
        }
        sc.close();
        return userInput;
    }

    public double FindInterval() {
        while (b * b < userInput) {
            b = b + 1;
        }
        return b;
    }

    public double RoundNumber(double number) {
        //Rounds number to 4 decimal places.
        String pattern = "#.####";
        DecimalFormat formatNumber = new DecimalFormat(pattern);
        double rounded = Double.valueOf(formatNumber.format(number));
        return rounded;
    }

    public double FindAnswer(double number, double interval1, double interval2) {

        midpoint = (interval1 + interval2) / 2;
        double difference = (midpoint * midpoint) - number;

        while (RoundNumber(difference) != 0) {
            midpoint = (interval1 + interval2) / 2;
            difference = (midpoint * midpoint) - number;
            if (midpoint * midpoint < number) {
                interval1 = midpoint;
            } else {
                interval2 = midpoint;
            }
            iteration = iteration + 1;
        }
        System.out.println("Iterations: " + iteration);
        return midpoint;
    }
}

Answer 1

Work toward understanding mathematics in programming well, is worth the effort. Check this post out as it might provide some elucidation why you are getting some unexpected values - maybe a little more complicated than you were aware. Programming problems only take tenacity to solve them, just keep plugging away.

Double vs. BigDecimal?

Answer 2

Change

while (RoundNumber(difference) != 0) {

To:

while (difference != 0) {

Or compare against a small epsilon:

while (Math.abs(difference) > 0.0000001) {