Time complexity of subset sum problem with reals instead?
What model of real numbers are you using?  If it's something like floating point, where everything is really rational, just multiply through by a common denominator and you're back in the world of integers. The bit-length is only polynomially larger than the ones you started with (the common denominator is at most the product of $n$ $n$-bit numbers, so it has at most $n^2$ bits), so nothing has changed, complexity-wise.

Beyond that, things will get more complicated&nbsp;&ndash; can you even tell in polynomial time what numbers are represented by the input?

However, the real-number version is definitely still NP-hard, since it has the integer version as a sub-problem.