Source: Extra Practice

The mass of a substance is measured as 4.237 g4.237\text{ g} and its volume is 2.51 cm32.51\text{ cm}^3. Calculate its density with due regard to the rules of significant figures.

Options

Option A is correct

1.69 g cm−31.69\text{ g cm}^{-3}

Option B

1.688 g cm−31.688\text{ g cm}^{-3}

Option C

1.7 g cm−31.7\text{ g cm}^{-3}

Option D

1.6882 g cm−31.6882\text{ g cm}^{-3}

Explanation

Density is calculated as Density=massvolume=4.237 g2.51 cm3≈1.688047 g cm−3\text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{4.237\text{ g}}{2.51\text{ cm}^3} \approx 1.688047\text{ g cm}^{-3}. In multiplication or division, the final result must be rounded off to the same number of significant figures as the term with the least number of significant figures. Here, the volume (2.512.51) has 3 significant figures, while the mass (4.2374.237) has 4. Therefore, the result must be rounded off to 3 significant figures, yielding 1.69 g cm−31.69\text{ g cm}^{-3}.