Why does num2str() of 138.97 return 138.96999999999999886?

I use num2str to set parameters into a Simulink model via set_param.

The parameters are sometimes irrational fractions (hence num2str(parameter,20)) makes sense, but some other times they are simpler values like 138.9. Therefore, to "work with all cases", I thought of using 20 digits all the time.

Then I noticed that num2str(parameter,20) does not add just zeros, but extra decimals. For example:

K>> A = 138.97;
K>> num2str(A,20)
ans =
    '138.96999999999999886'

K>> num2str(A,'%20.20f')
ans =
    '138.96999999999999886313'

Why does this happen?

I would expect that either setting the number of digits or the format spec would just fill the string with extra zeros.

Answer 1

[dpb]

Wrong expectation for floating point numbers -- short story is if a fraction is not exactly representable by 1/2^n, it'll not be able to be stored exactly and so what you get is the closest representation that can be stored.

All the skinny is in <Goldberg, What Every Computer Scientist...>>

If you want only n digits of precision past the decimal point, set that in the format string.

I don't know anything about Simulink; can't you pass the actual variable into it, not a string? Then you get the closest binary representation without any rounding, whatever the value. All it's going to do with the string is convert it back to internal representation, anyway.