I hope you are measuring the battery voltage while the voltage divider is also in place.
Batteries have an internal resistance. Because of that the voltage as measured on a battery can depend on what is attached.
Many DVMs have a battery check mode which inserts a small load. The older needle-type voltmeters also have lower input resistance.
A "ideal" battery has 0 ohms internal resistance and the ideal voltage measurement meter has infinite resistance.
Also, you might scale up your resistor values. Why constantly waste 1+ milliamps. The arduino has much higher input impedance.