fft and inverse fft error size and applying impulse response matlab I have a signal called noise. I am using the following command to calculate the mean squared error after fft and inverse fft process:

 sum((noise-real(ifft(fft(noise,2048),num_of_samples))).^2)/num_of_samples


Where num_of_samples=2819519 is the number of samples in the original signal. 
I am getting an error of $\sim10^{-8}$. Is that reasonable and due to approximation or does that indicate something is not converted correctly? 

My final goal is to multiply the signal in the frequency domain with a $1052\times 4$ given impulse response. This represents a room with 4 microphones.
I don't know your overall goal but if you want to test the MSE associated with FFT / IFFT then you should perform the following

num_of_samples = 2819519 ;
fft_len         = 2^nextpow2(2819519) ;

X = fft(signal, fft_len);
y = real( ifft(X, fft_len) );
mse = sum( (signal - y(1:num_of_samples) ).^2 )/num_of_samples