9.74 g of a substance occupies 1.2 cm³. Express its density by keeping the significant figures in view.

The correct option is 8.1 g cm^-3.

To find the density of the substance, we use the standard formula for density, which is defined as mass per unit volume:
$$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$$

From the given data:
Mass of the substance = 9.74 g (which has 3 significant figures)
Volume occupied = 1.2 cm³ (which has 2 significant figures)

Substituting these values into the density formula:
$$\text{Density}=\frac{9.74\text{g}}{1.2{\text{cm}}^3}\approx \mathrm{8.1166...}{\text{g cm}}^{-3}$$

According to the rules of significant figures, when performing multiplication or division, the final result must be rounded off to keep the same number of significant figures as the measurement with the fewest significant figures.
Here, the volume (1.2 cm³) has the least number of significant figures, which is 2. Therefore, our final density value must be rounded to 2 significant figures.
Rounding 8.1166... to two significant figures gives:
$$\text{Density}=8.1{\text{g cm}}^{-3}$$