How should you saw a block of stone of 40 kg into four pieces such that you can measure all weights of an integer from 1 kg to 40 kg (so 1 kg, 2 kg, 3 kg, 4 kg, ..... 39 kg and 40 kg) on a balance?

You should saw the block of stone in a piece of 1 kg, a piece of 3 kg, one of 9 kg and one of 27 kg.