Wrong readings from voltage divider

I forgot to mention that this point:

dc42:
2. If you feed the ADC from a source resistance of more than 10K, then you need to take precautions to prevent the increased source resistance affecting the reading. There are two simple ways of doing this. One is to connect a capacitor of 0.01uF or greater between the analog pin and ground. This has the side effect of slowing down the rate of change of the signal, but this is acceptable in some applications. The other is to introduce a delay in the code for analogRead() between selecting the input channel and starting the conversion. The delay needed is about 1us per additional 10K source resistance.

is most relevant if you are using 2 or more analog input pins. If you only ever read from one analog pin, then after the first reading the internal multiplexer is always set to that pin, in which case the effects of using a high source resistance are much reduced.