### Theory:

The density of a particular substance, under specific conditions, remains the same. Therefore, the density of a substance is one of its characteristic properties. It is different for different substances.

For example, the density of gold is 19300 $\mathit{kg}/{m}^{3}$, while that of water is \(1000\) $\mathit{kg}/{m}^{3}$. The density of a given sample of a material can help us to determine its purity. It is easy to express the density of a substance in comparison with that of water.

For example, the density of gold is 19300 $\mathit{kg}/{m}^{3}$, while that of water is \(1000\) $\mathit{kg}/{m}^{3}$. The density of a given sample of a material can help us to determine its purity. It is easy to express the density of a substance in comparison with that of water.

*Relative density*

The relative density of a substance is the ratio of its density to that of water.

$\mathit{Relative}\phantom{\rule{0.147em}{0ex}}\mathit{density}=\frac{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}a\phantom{\rule{0.147em}{0ex}}\mathit{substance}}{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{water}}$

The relative density has similar quantities in numerator and denominator. Therefore, it has no unit.

**Example**:

**1**. The density of water is ${10}^{3}$ $\mathit{kg}/{m}^{3}$. Find the density of silver, whose relative density is \(10.8\).

**Given data**:

Relative density of gold \(=\) \(10.8\)

Density of water \(=\) ${10}^{3}$ $\mathit{kg}/{m}^{3}$

**To find**: Density of the material

We know,

$\mathit{Relative}\phantom{\rule{0.147em}{0ex}}\mathit{density}=\frac{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}a\phantom{\rule{0.147em}{0ex}}\mathit{substance}}{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{water}}$

Apply the known values,

$\begin{array}{l}10.8=\frac{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{gold}}{{10}^{3}}\\ \mathit{By}\phantom{\rule{0.147em}{0ex}}\mathit{simplifying},\\ \mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{gold}=10.8\times {10}^{3}\mathit{kg}/{m}^{3}\end{array}$