6*0.003125 - 0.018750 = 0, right? How to get the right answer?

In Matlab >> 6*0.003125

ans =

   0.018750000000000

>> 6*0.003125 - 0.01875

ans =

     3.469446951953614e-18

In Mathematica

In[17]:= 6*0.003125 6*0.003125 - 0.018750

Out[17]= 0.01875

Out[18]= 3.46945*10^-18

~~~~~~~~~~~~~~~~~~~~~~~~~~~How can I get the right answer??

Answer 1

[Walter Roberson]

Matlab is giving you the right answer. Matlab uses IEEE 754 binary floating point double precision. Floating point operations are not algebraic and not generally commutative.

In binary floating point there is no exact representation of 0.1, just the same way that in base 10 there is no way to exactly represent 1/7 in any finite precision decimal number.

Answer 2

[Thorsten]

You can compare the results against the machine precision eps and regard them as equal if smaller than eps

6*0.003125 - 0.01875 < eps

[hogeol lim]

I finally understand the equal in case using computer, Thank you.

Answer 3

[Steven Lord]

For a more in-depth answer to this general situation, with many references, see question 1 in the Mathematics section of the FAQ.

[hogeol lim]

Thank you for introduction of MatlabWiki site