The composition of a mixture can be expressed by comparing the amount of one component with the total amount of mixture. Different measures are useful because mass, amount of substance and volume answer different questions.

For component $i$, the mass fraction is

$$w_i=\frac{m_i}{m_{\mathrm{total}}}.$$

The mass fractions of all components sum to one. Multiplying by $100%$ gives mass percent.

For example, a solution prepared from $5.0,\mathrm g$ of salt and $95.0,\mathrm g$ of water has total mass $100.0,\mathrm g$, so

$$w_{\mathrm{salt}}=\frac{5.0}{100.0}=0.050,$$

or $5.0%$ salt by mass.

The mole fraction is

$$x_i=\frac{n_i}{n_{\mathrm{total}}},$$

and the mole fractions also sum to one. Mole fraction is especially useful when molecular counts rather than masses control the physics.

Liquid and laboratory mixtures are also often reported with explicitly labeled percentage conventions:

$$%,(m/m)=\frac{m_{\mathrm{solute}}}{m_{\mathrm{solution}}}\times100%,$$

$$%,(V/V)=\frac{V_{\mathrm{component}}}{V_{\mathrm{solution}}}\times100%,$$

and

$$%,(m/V)=\frac{m_{\mathrm{solute}}\text{ in grams}}{V_{\mathrm{solution}}\text{ in mL}}\times100.$$

Thus a $2.0%,(m/V)$ solution contains $2.0,\mathrm g$ of the stated solute per $100,\mathrm{mL}$ of final solution.

Very small fractions are often expressed using parts per million or parts per billion:

$$1\ \mathrm{ppm}=10^{-6},\qquad 1\ \mathrm{ppb}=10^{-9}.$$

A mass fraction of $2.5\times10^{-6}$ is therefore $2.5,\mathrm{ppm}$ by mass.

The basis must be stated whenever it is not obvious. Mass fraction, mole fraction, volume percentage and mass-per-volume percentage are different quantities and generally have different numerical values. These measures apply to mixtures broadly, including solutions, gas mixtures and alloys.