trying to understand why I get 2.2204e-16 rather than 0
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Im trying to understand why when i make x-y (where x=1.6 and y=1.6) i do not get 0 as a result.
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DGM
on 28 Aug 2021
Edited: DGM
on 28 Aug 2021
Simply put, the assumption that both x and y are equal to the same value is incorrect. One or both have accumulated rounding error in some undescribed process.
% x and y are assigned the same value
x = 1.6;
y = 1.6;
x-y
% y has accumulated some rounding error
k = pi;
y = k*(y/k);
x-y
% the difference is nonzero, but they look the same
[x y]
% but that's just because the error is small relative to the nominal value
[x y]-1.6
Not all numbers can be represented exactly in base 2, just as not all numbers (e.g. 1/3) can be represented exactly in base 10.
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Walter Roberson
on 28 Aug 2021
Minor correction: all rational numbers can be represented exactly in base 2 or base 10 -- but it might take infinite precision to do so!! Since there is only a finite amount of resources in the universe, what we can represent in base 2 or base 10 in a computer is finite length rather than infinite length, not all rational numbers can be represented in base 2 or base 10 in a computer .
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