In fact in this case, it's not the known limitation of floating point numbers to blame: this Calculator application gives you the ability (submenu under View > Decimal Places) to choose a precision between 0 to 15 decimal places, and it will do rounding beyond that point. I think the default is 8.

The original screenshot shows a number with 13 decimal places, and if you set it at or above 13, then the calculation will come out correct.

The application doesn't really go out of its way to communicate this to the user. For the most part maybe it doesn't matter, but "user entering more decimal places than they'll get back" might be one thing an application might usefully highlight.