Voltage divider to sense voltage on arduino
The ATmega based Arduino boards (ATmega328P for instance) use a capacitive sample and hold circuit for the ADC inputs. This has two implications for your applications:


There is a delay between initialization of the ADC and availability of a stable analog datum
While overall input impedance of the ATmega328P is stated in the datasheet as 100 MOhms, the actual current drawn for charging the sampling capacitor requires an output impedance of the order of 10 kOhms from your signal source, for fast stable analog reading.


To address the first issue try the AnalogRead() 3 or 4 times in a row, and see whether the final value stabilizes to the range you expect. Just discard the first few readings each time around. 

For the second issue, a 10 k / 1 k voltage divider should work better: This will however draw more current (4.545 mA), and hence the 10 kOhm resistor needs to be rated for more than 207 mW. So a half-watt resistor would be my choice. After doing this, you may be able to obtain stable AnalogRead() results without having to delay on the reading, so the previous point becomes void. 

A third issue to consider: Is there a capacitor on the voltage divider messing up the works, by any chance? If so, remove that capacitor.