function eps02f
clc;
kmax = 100;
fprintf('Approximation for 3 Decimal Digit Machine Epsilon:')
eps0 = 1./100;
eps1 = f02d(eps0 + 1);
for k = 1:kmax 	
	epssv = eps0;    
	eps1sv = eps1;	
	ks = k - 1;    
	eps0 = 1./100-(k-1)*(1./10^3);  % subtracting .001 has too much truncation
	eps1 = f02d(eps0 + 1);    
	fprintf('\n  k = %4i; eps0 = %f; eps0+1 = %f;',k,eps0,eps1)
	if eps1 <= 1.e0
		break;  	
	end 
end
fprintf('\nApproximation Answer for 3 Decimal Digit Precision:')	
fprintf('\n k = %4i; epssv = %f; epssv+1 = %f;', ks, epssv, eps1sv)	
prec = 1-log(epssv)/log(10.); % find prec if maceps = 10^(1-prec);
fprintf('\nprecision = %f decimal digits', prec)
fprintf('\nCheck It Out!!!?:')
fprintf('\n eps0 = %15.7e; 1+eps0 = %f; BUT 100.5-(1+0.005)*100 = %e' ...
    ,eps0,1+eps0,100.5-(1+0.005)*100)
fprintf('\nIs the Class Theoretical Value?:')
% check for rounding through refinement: 
fprintf('\n\nRounding Test Data:')
eps0 = 0;
deleps = 10^(-prec); % start with bisection maceps/4;
fprintf('\n deleps = %f;', deleps); 
for k = 1:15  
	eps0 = eps0 + deleps;   
	eps1 = f02d(eps0 + 1);   
	fprintf('\n k = %4d; eps0 = %f; eps0+1 = %f', k, eps0, eps1)
end
fprintf('\nIs Rounding or Chopping Demonstrated?:\n')
% end MATLAB main function
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
function y = f02d(x)
y = round(x*10^2)/10^2;



%=================================OUTPUT=====================================
%>> Approximation for 3 Decimal Digit Machine Epsilon:
%  k =    1; eps0 = 0.010000; eps0+1 = 1.010000;
%  k =    2; eps0 = 0.009000; eps0+1 = 1.010000;
%  k =    3; eps0 = 0.008000; eps0+1 = 1.010000;
%  k =    4; eps0 = 0.007000; eps0+1 = 1.010000;
%  k =    5; eps0 = 0.006000; eps0+1 = 1.010000;
%  k =    6; eps0 = 0.005000; eps0+1 = 1.000000;
%Approximation Answer for 3 Decimal Digit Precision:
% k =    5; epssv = 0.006000; epssv+1 = 1.010000;
%precision = 3.221849 decimal digits
%Check It Out!!!?:
% eps0 =  5.0000000e-003; 1+eps0 = 1.005000; BUT 100.5-(1+0.005)*100 = 1.421085e-014
%Is the Class Theoretical Value?:
%
%Rounding Test Data:
% deleps = 0.000600;
% k =    1; eps0 = 0.000600; eps0+1 = 1.000000
% k =    2; eps0 = 0.001200; eps0+1 = 1.000000
% k =    3; eps0 = 0.001800; eps0+1 = 1.000000
% k =    4; eps0 = 0.002400; eps0+1 = 1.000000
% k =    5; eps0 = 0.003000; eps0+1 = 1.000000
% k =    6; eps0 = 0.003600; eps0+1 = 1.000000
% k =    7; eps0 = 0.004200; eps0+1 = 1.000000
% k =    8; eps0 = 0.004800; eps0+1 = 1.000000
% k =    9; eps0 = 0.005400; eps0+1 = 1.010000
% k =   10; eps0 = 0.006000; eps0+1 = 1.010000
% k =   11; eps0 = 0.006600; eps0+1 = 1.010000
% k =   12; eps0 = 0.007200; eps0+1 = 1.010000
% k =   13; eps0 = 0.007800; eps0+1 = 1.010000
% k =   14; eps0 = 0.008400; eps0+1 = 1.010000
% k =   15; eps0 = 0.009000; eps0+1 = 1.010000
%Is Rounding or Chopping Demonstrated?:
%>>