the number of significant figures An electronic balance was used to determine that a sample has a mass of 9.00060 g.  If the balance's precision is ± 1 mg, what is the correct number of significant figures for this measurement?
actually the answer is 4 but I cant figure out from where has it come from? Isn't it 5?
The significant digits you use are the values of which you are confident, plus one more value which may be uncertain.

In this case, the balance is accurate to $\pm0.001$ mg, so you're confident about the first 2 decimal places, but the 3rd place is uncertain.

The measurement given is $9.00060$, but the decimal part is smaller than our uncertainty, so we can't count on it.  The most accurate we could record is $9.001$, because the first decimal we're uncertain about is the 3rd place, which leaves us 4 significant figures.

If the measurement had been $19.00060$ instead, then the same process would result in 5 significant figures.