comparison of double numbers

I just try to compare two double numbers:

q = 0.1:0.05:0.7;
q(2) == 0.15

I have "false". Ok, print this number into "txt" file:

fprintf(fileID,'%99.99e\n',q(2));

And i see follow:

1.500000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01

Why the "2"(exactly)?

[Wayne King]

Why the "2" exactly? Can you clarify?

Answer 1

[Jan]

An evergreen question.

See FAQ: Why is 0.3 - 0.2 ~= 0.1

You find over a hundred of related posts in this forum, when you search for "faq6.1".

Matlab (as other numerical software) stores the values as IEEE 754 format using 64 bits. Printing 99 decimals does not reveal the underlying limitation, that not all decimal numbers have an exact binary representation.

[Pavel]

OK, thank you!

[Jan]

You are welcome, Pavel. This problem is not intuitively clear to beginners in numerical computations. But it is fundamental and appears such frequently, that it should appear 8 times in the FAQ. But even then it is a well known phenomenon, that the FAQ is not read by beginners, but maintained by profis.

[Walter Roberson]

There is a bug in MATLAB's fprintf() on MS Windows that causes it not to print out all the decimal places. Please see the FEX contribution num2strexact