num2str, accuracy, precision, rounding error

Please have a look at this code ...

b = 1.00000001;
a = num2str(b,'%.100f')
a = 1.0000000099999999000000000000000000000000000000000000000000000000000000000000000000000000000000000000
a = num2str(b,'%.10f')
a = 1.0000000100

Why is the result different?

How to obtain the right result in the first case?

Answer 1

[Jyotish Robin]

Hi Lu,

By default, MATLAB stores all numeric values as double-precision floating point. The fact is, almost all decimal numbers are NOT representable exactly in floating point arithmetic as a double. This is why this issue is completely about precision and the binary form that a double comprises.

You can read in detail about this here: http://stackoverflow.com/questions/10904132/conversion-of-numeric-to-string-in-matlab

If you are interested in converting a double or single input to the exact decimal string, you could refer the following file exchange submission: https://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact--exact-version-of-num2str-

Hope the above suggestions help!