Wavelet Transform Output in MATLAB

I have a question regarding the output of performing a wavelet transform in MATLAB on an audio signal. I have an audio signal imported into MATLAB using the `wavread` function. I then perform a one level wavelet transform on the signal using the `wavdec` function (usually a haar or db4 transform). To transform the signal back to the original audio signal, I then perform an inverse wavelet transform on the signal using the function `wavrec`. The output of this function brings me back to the original audio signal. However, many data points are slightly off from the original signal (only by about a magnitude of 10^-16 so it is very slight). However, in theory the inverse transform should give me the exact original signal. I am not sure if I am doing something wrong, but is there a reason that after performing a wavelet transform and then performing the inverse that I am not getting an output of exactly the original signal? Thank you very much for any help!