O'Scopes are very wideband devices and noise is everywhere and dictated by physics for high impedance sources like a scope probe. Use a real 10x scope probe if you can, minimize any loop area as AG6QR noted. The "ripple" on a pure DC source should be as good as it gets- a test is to short the probe with the shortest path possible, limit the BW to 20 MHz and look at the results- you shouldn't see more than 10 mV. The noise inherent in a 10 M-Ohm resistive source is about 1.8 mV in a 20 MHz bandwidth. This is RMS, the peaks you might see are less than 12 mV. This is Johnson noise and is an inescapable fact of life. The 1052E uses an 8 bit analog to digital converter- this gives a basic (quantization error- physics limited) noise level in dB of 6.02B + 1.76. For 8 bits, this is ~50 dB or about +-.3%- this gets added to the Johnson noise above. If you're on a 100 mV AC scale, with BW limited to 20 MHz, you should see something like 1.8 mV from Johnson and .3 mV from quantization- peak to peak could be 15 mV. If you don't limit BW, the 1052 would have 50 Mhz of BW that would see about 3mV RMS of Johnson noise. The peaks of this noise are almost always less than 6x RMS or 20 mV - either way, you shouldn't be seeing noise approaching 30 mV if you have a decent connection to the source without loops. There are some other minor error sources (sin(x)/x interpolation and excess noise) but that's about it. You should be able to resolve 30 mV easily with a reasonable setup. Rigol doesn't specify a noise value but you can get a pretty good handle from first principles. A good test to see if the scope is right it to put a terminator on the input- 50 ohms doesn't produce much Johnson noise, this should be pretty quiet.