1.1 + 0.1 == 1.2 returns false

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N/A
N/A 2014-1-13
评论： James Tursa 2014-1-31
Very strange.
Apparently this is related to the precision of the double type as
1.1 + 0.1 - 1.2 = 2.2204e-16
What can I do to counter this behavior? Thanks!
  1 个评论
James Tursa
James Tursa 2014-1-31
As a learning aid you can use this FEX submission to see the exact numbers involved:
http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str
E.g., for your example,
>> num2strexact(1.1)
ans =
1.100000000000000088817841970012523233890533447265625
>> num2strexact(0.1)
ans =
0.1000000000000000055511151231257827021181583404541015625
>> num2strexact(1.1+0.1)
ans =
1.20000000000000017763568394002504646778106689453125
>> num2strexact(1.2)
ans =
1.1999999999999999555910790149937383830547332763671875

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采纳的回答

Image Analyst
Image Analyst 2014-1-13
编辑：Image Analyst 2014-1-13
See the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F It has strategies to deal with this situation, such as comparing the value to a tolerance.
% instead of a == b
% use:
areEssentiallyEqual = abs(a-b) < tol
% for some small value of tol relative to a and b
% perhaps defined using eps(a) and/or eps(b)
  2 个评论
N/A
N/A 2014-1-30
Interesting, Surprising that there isn't some native function that takes care of this. Thanks!
Roger Stafford
Roger Stafford 2014-1-31
编辑：Roger Stafford 2014-1-31
In both matlab and on my calculator these quantities come out unequal:
(sqrt(2))^2 ~= 2
(3/14+15/14)+3/14 ~= 1.5
The reason is quite clear. The quantities on the left hand side involve fractional values that cannot be represented exactly either on matlab's computer or on a decimal calculator. But when it comes to
11/10+1/10 and 12/10,
as in the case you mentioned, the calculator has them exactly equal but matlab doesn't. Why is that? It is because the calculator is using decimal digits and the computer is using binary digits - even though matlab normally displays numbers in decimal form, it is actually performing the computation with numbers in binary form. There is no way matlab could be programmed to obtain an exact equality in all such cases when division by something other than powers of 2 are involved. For that reason you cannot expect exact equality where, for example, division by 10 is involved. This is the binary computing world you have entered.

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更多回答（2 个）

Azzi Abdelmalek
Azzi Abdelmalek 2014-1-13
Mischa Kim
Mischa Kim 2014-1-13
编辑：Mischa Kim 2014-1-13
MATLAB is a numerical software tool, not an algebraic one. What you are seeing there is the numerical accuracy measure called eps. In other words, this is as accurate as your results will get.

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