MATLAB Answers

Numerical errors of basic multiple

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yifwang
yifwang on 26 Aug 2019
Commented: yifwang on 26 Aug 2019
When using matlab multiple calculation, some errors happen
a = 7*13e-6;
b = 6*13e-6;
the answer is
a = 9.09999999999999999e-5
b = 7.80000000000000000e-5
erroe happened at a but not at b;
So how this error happen and how * works? On what condition the error happen?

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KALYAN ACHARJYA
KALYAN ACHARJYA on 26 Aug 2019
Error?
>> a =13e-6
a =
1.300000000000000e-05
>> 7*a
ans =
9.099999999999999e-05
yifwang
yifwang on 26 Aug 2019
7*13e-6 should be exactly
9.100000000000000e-5
but not
9.099999999999999e-5
error

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Accepted Answer

Ted Shultz
Ted Shultz on 26 Aug 2019
These are floating point calculations. Not every number can be represented, and this rounding error can compound when you do math with these imperfect numbers.
"Floating-point error arises because real numbers cannot, in general, be accurately represented in a fixed space."

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