How to check equality of very small numbers ?

Hey Community !!

I have two very closely related numbers

A = 1.309998142150646e-09
B = 1.309998162564509e-09

now if i need to compare two numbers only upto 5 precision points , i.e.

A = 1.309998e-09 %how can i get this from above mentioned A
B = 1.309998e-09

now my condition A == B will satisfy,

so what can i do to check if both numbers are equal upto 5 precision points, keeping the exponential part ?

Answer 1

[Stephen23]

A = 1.309998142150646e-09;
B = 1.309998162564509e-09;

Method one: compare the absolute difference against a tolerance:

tol = 1e-14;
abs(A-B)<tol

ans = logical
   1

Method two: use ISMEMBERTOL (the 3rd argument specifies the relative tolerance):

ismembertol(A,B,1e-5)

ans = logical
   1

Do NOT round the values, as this introduces artifacts into the data:

https://www.mathworks.com/matlabcentral/answers/321709-strange-behaviour-of-matlab-find-command#comment_444258

https://www.mathworks.com/matlabcentral/answers/350303-why-0-6-is-not-equal-to-0-2-3#comment_472139