Question

The density of an object is defined as its mass divided by its volume. Suppose a rock’s mass and volume are measured to 6 g and$2.8325{\mathrm{cm}}^3$. To the correct number of significant figures, determine the rock’s density (mass/volume).

Short answer

The density of the rock up to one significant figure is $2\mathrm{g}{\mathrm{cm}}^{-3}$.

Step-by-step solution

Step 1. Definition of significant figures

Significant figures give the exact count of digits in a number. For determining the number of significant figures, zeroes are treated as place holders.

Step 2. Identification of the given data

Mass of the rock,$m=6\mathrm{g}$

Volume of the rock,$V=2.8325{\mathrm{cm}}^3$

Step 3. Determination of the density of the rock

The density of an object is mass per unit volume.

$D=\frac{m}{V}$

The mass of the rock has only one significant figure, whereas the volume of the rock has five significant figures.

The density of the rock, keeping the least number of significant figures, is:

$\begin{array}{c}D=\frac{6\mathrm{g}}{2.8325{\mathrm{cm}}^3}\\ =2\mathrm{g}{\mathrm{cm}}^{-3}\end{array}$

Thus, the density of the rock up to one significant figure is $2\mathrm{g}{\mathrm{cm}}^{-3}$.