How to Determine Round-Off Error in a C++ Program?

[ZachN]

Homework Statement

Not a homework just self-teaching. I want to write a program which determines the round-off error of a number.

Homework Equations

r_e = Abs(x-x*)<= 0.5x10^(n-2)

x*-0.5x10^(n-2) < x < x* + 0.5x10^(n-2)

The Attempt at a Solution

#include <iostream>
#include <cmath>
using namespace std;

int k, n; //Declares variables k and n.
double x, x_ro, sub_x, sup_x; //Declares variables x and x*.

int main()
{
cout << "Enter a number.\n";
cin >> x;
cout << "Enter the desired number of significant digits.\n";
cin>> k;
cout << "Enter the rounded-off number.\n";
cin >> x_ro;

int n;
for (n == 0; n == -10; n--)
{
sub_x == x_ro - .5 * pow(10, n - k);
sup_x == x_ro + .5 * pow(10, n - k);
cin >> n;

if (x >= sub_x && x <= sup_x) //To check that condition is met
{

break;
cout << "n = " << n;
}
}

for (n == 0; n == 10; n++)
{
sub_x == x_ro - .5 * pow(10, n - k);
sup_x == x_ro + .5 * pow(10, n - k);
cin >> n;

if (x >= sub_x && x <= sup_x)
{

break;
cout << "n = " << n;
}

}

return 0;
}

 

[ZachN]

No one can offer even a suggestion? Maybe my code is a bit confusing.