What would you suggest to a student if while performing an experiment he finds that the pointer/needle of the ammeter and voltmeter do not coincide with the zero marks on the scales when the circuit is open?

Now first of all you need to get the least count of both meters. Then add as many least counts as needed to add up to the point where the needle coincides. It is a little about measurement error. Just subtract the initial reading of the open circuit from the reading when you perform the experiment. Actual reading = Final reading - Initial reading