Question

what does it mean to weigh to the nearest 0.001g? does that mean there will be three signficant figures for the measurement?

Answer 1

1 mg = 0.001 g

So, weighing to the nearest 0.001 g means, weighing to the nearest milligram. This doesn't mean there will be three significant figure. The weight could be anything like this-

0.005g 1 significant digit

0.013g 2 significant figures

0.117 g 3 significant figures

1.234 g 4 significant figures and so on

You just have to weigh to the nearest milligram. For example if you get the weight to be 0.0136789g, round it to three decimal places which is 0.014g.

Comment if still in doubt.