Bought DS1104Z-S for the company, a couple of things pissed me off right away...
1. The channel zero marker on the left is lower than the GND level, by as much as 0.2 grid height, it's painfully visible.
Welcome to the physical world, where
all devices have specified tolerances and are less than 100% perfect.
Your chosen device's specifications are:
DC Offset Accuracy: ±0.1 div ±2 mV ±1% offset value
DC Gain Accuracy: <10 mV: ±4% full scale ?10 mV: ±3% full scale
Do a self-calibration and see if it improves a bit. Remember; the DC offset may change with temperature so you have to switch it on and leave it for half an hour in the place you intend to use it before you do the self-calibration. You also have to warm it up to that exact temperature before the voltage readings will be within the spec above.
In practice a tiny bit of DC offset doesn't matter:
a) The primary function of an oscilloscope is to look at the
shape of signals and to
see how they vary with time.
b) The 'low' signal put out by your devices probably isn't 0.000000V anyway, it's just 'low'.