Assuming that we have a sensitive electronics that is battery powered, which consist of a very sensitive 32 bit adc is reading a voltage from a chemical reaction and you place it inside a chunky 1 inch thick metal shielding (I could not think of a better example). The circuit inside is built to the best ideal configuration. Would connecting the metal shield to the circuit's ground inside affect the result or its best to leave the circuit inside floating to best protected from whatever stray interference.
What if this time the the electronics inside is powered from mains voltage via a wall power adaptor. The metal shielding is still there but this time from the wall power adaptor 2 wires is passed through to the thick metal shielding to give power to the circuit inside. Would connecting the metal shielding to ground now a must?