calculation with numbers with maximum 3 nonzero digits gives a result with more then 3 nonzero digits

can someone explain me why a calculation with numbers with maximum 3 nonzero digits gives a result with more then 3 nonzero digits:

num2str(0.541*16.0,'%2.30f')

ans =

8.656000000000000600000000000000

Thanks!

Answer 1

[Fangjun Jiang]

This is the limitation of using limited number of binary numbers to represent a real-word value. Even with double precision (8 bytes or 64 bits) floating point data type, it's still impossible to represent every real-world value without errors.

>> num2str(0.541,'%2.30f')
ans =
0.541000000000000040000000000000
>> num2str(16,'%2.30f')
ans =
16.000000000000000000000000000000

[Walter Roberson]

Yep.

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[Lucian]

Thank you for the answer. By the IEEE 754 norm, shouldn’t matlab or the computer be able to use exact representations and do exact simple operations also, with some real numbers with small finite representations in base 10 and not do it all the time with their representations in base 2?

[Lucian]

Look, for example, at MATLAB trying to do a base 2 representation of 0.1:

0.10000000000000001000

0.20000000000000001000

0.40000000000000002000

0.80000000000000004000

1.60000000000000010000

1.20000000000000020000

0.40000000000000036000

0.80000000000000071000

1.60000000000000140000

1.20000000000000280000

0.40000000000000568000

0.80000000000001137000

1.60000000000002270000

1.20000000000004550000

0.40000000000009095000

0.80000000000018190000

1.60000000000036380000

1.20000000000072760000

0.40000000000145519000

0.80000000000291038000

1.60000000000582080000

1.20000000001164150000

0.40000000002328306000

0.80000000004656613000

1.60000000009313230000

1.20000000018626450000

0.40000000037252903000

0.80000000074505806000

1.60000000149011610000

1.20000000298023220000

0.40000000596046448000

0.80000001192092896000

1.60000002384185790000

1.20000004768371580000

0.40000009536743164000

0.80000019073486328000

1.60000038146972660000

1.20000076293945310000

0.40000152587890625000

0.80000305175781250000

1.60000610351562500000

1.20001220703125000000

0.40002441406250000000

0.80004882812500000000

1.60009765625000000000

1.20019531250000000000

0.40039062500000000000

0.80078125000000000000

1.60156250000000000000

1.20312500000000000000

0.40625000000000000000

0.81250000000000000000

1.62500000000000000000

1.25000000000000000000

0.50000000000000000000

1.00000000000000000000

0.00000000000000000000

0.00000000000000000000

0.00000000000000000000

0.00000000000000000000

0.00000000000000000000

my problem is that a guy with a pocket computer did it better, without errors and even correct me.