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str2double conversion error

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John Jendzurski
John Jendzurski on 30 May 2020
Edited: Adam Danz on 30 May 2020
Is there a way to avoid this sort of error/effect (see code below) when converting a string to a double? I have tried using str2num() but get the same result.Thanks!
>> str2double('39.11237316')
ans =
39.112373159999997

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Accepted Answer

Adam Danz
Adam Danz on 30 May 2020
Edited: Adam Danz on 30 May 2020
You're witnessing floating point roundoff error. In short, an infinite range of numbers must be represented in a finite number of bits (specifically, 64 for double precision numbers). The number you're trying to represent doesn't fit perfectly in this system so it's rounded.
Check this out.
format long
x = 39.11237316
% x =
% 39.112373159999997
% Even if you round it to 8 dp, it can't be represeneted
round(x,8)
% ans =
% 39.112373159999997
So, it's not the str2double() that is the problem, it's the finite precision that this number can be represented in.
If higher precision is required you can use symbolic representation for your computations. But the difference between your value and the value being represented is very tiny and usually not a problem.
For a wonderful explanation of floating point roundoff error, see Cleve Moler's article (founder of Matlab).

  2 Comments

John Jendzurski
John Jendzurski on 30 May 2020
That's a very helpful, clear, and excellent description of what is happening. Thanks, Adam!
Adam Danz
Adam Danz on 30 May 2020
Thanks for the feedback, John. Glad I could help.

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