Weird results while coding using an m-file

Hi,

When using the following code, I expect A = B. The difference (Differ) is however not zero. Any clue?

Thanks

clear all, clc
Vs = 10;
R = 10;
L = 10e-3;
C = 400e-6;

A = (R/(2*L))^2
B = 1/(L*C)
%B = 2.5000e+05
Differ = A-B

Answer 1

[Voss]

This is an effect of floating-point arithmetic.

Related: https://www.mathworks.com/matlabcentral/answers/57444-why-is-0-3-0-2-0-1-not-equal-to-zero

See also: https://www.mathworks.com/help/matlab/ref/eps.html

Note that Differ == eps(A), which means that A and B are as close as they can be without being exactly equal.

Vs = 10;
R = 10;
L = 10e-3;
C = 400e-6;
A = (R/(2*L))^2

A = 250000

B = 1/(L*C)

B = 2.5000e+05

Differ = A-B

Differ = 2.9104e-11

eps(A)

ans = 2.9104e-11

eps(A) == Differ

ans = logical
   1

[Rimon]

Thank you for this detailed explanation. How can I however overcome this issue?

[Voss]

Don't expect Differ to be exactly zero.

When comparing two floating point numbers, don't check for exact equality, use a small tolerance, e.g., abs(A-B) <= 10*eps(A)

or ismembertol

Or use the Symbolic Math Toolbox, e.g. vpa.