How to check equality of very small numbers ?

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Sajid Afaque
Sajid Afaque 2022-2-16
编辑： Stephen23 2022-2-16
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 ?

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Stephen23
Stephen23 2022-2-16
编辑：Stephen23 2022-2-16
Ran in:
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

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