The mass of a body is 275.32 g and its volume is 36.41 cm³ . Express its density upto appropriate significant figures.

The correct option is 7.562 g cm³.

Step-by-Step Explanation:

To find the density of the body with the appropriate number of significant figures, we use the standard formula for density:
$$\mathrm{Density}=\frac{\mathrm{Mass}}{\mathrm{Volume}}$$

From the given data:
Mass of the body = 275.32 g (which has 5 significant figures)
Volume of the body = 36.41 cm³ (which has 4 significant figures)

According to the rules of significant figures, when dividing or multiplying measurements, the final result must be rounded to the same number of significant figures as the measurement with the least number of significant figures. Here, the volume has the fewer significant figures (4 significant figures). Therefore, the final density must be expressed to exactly 4 significant figures.

First, we perform the division:
$$\mathrm{Density}=\frac{275.32}{36.41}\approx 7.56165888{\text{g cm}}^{-3}$$

To round 7.56165888 to 4 significant figures, we look at the fifth digit (which is 6). Since 6 is greater than or equal to 5, we round up the preceding fourth digit (1) to 2. This gives:
Density = 7.562 g cm³ (expressed to 4 significant figures)