If you measure the mass of a liquid is 11.50 g and its volume as 9.03 ml how many significant figures should its density value have

To get a result with the best degree of precision, the number of significant figures should be equal to the smallest number of significant figures of the given numbers. In this case, the smallest is 3 as given by the number 9.03 mL.

Therefore density is:

11.50 g / 9.03 mL = 1.27 g/mL

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