Mass and volume are quantities (properties that can be measured). Each quantity has a
symbol, a number and a unit.
For example, mass has the symbol m and may have units g or kg or mg.
The mass of a cup of water would be reported as m(H2O) = 250 g (quantity = number × unit)
A quantity is meaningless without its unit, because, for example, 250 g is a much smaller mass than 250 kg. Therefore, you must use numbers together with their units in all calculations.
Quantities may also be calculated by the combining of two measurements by multiplication or division.
Density is such a quantity. Density is a measure of mass per unit volume and is calculated by dividing mass by volume. The unit for density is also the unit of mass divided by the unit of volume.
The unit is shown for a mass in grams and a volume in L. It is convenient to write the unit on one line. " g L–1" is read grams per litre. Note that 1/L = L–1 just like 1/2 = 2–1. Try this on your calculator using the x–1 function.
Units can be used to decide whether your calculation will give the desired quantity.
Before entering the numbers into your calculator, it is helpful to check whether the units of the quantities that you have substituted into a mathematical relationship cancel to give the unit of the quantity that you want to calculate. Below are some guidelines for combination of units.
Example 1: Example 2: L × g
L–1 = g
- Units to the same power in the numerator and denominator cancel.
Thus g cancels as shown in the Example 1 at the right.
- The sign of the exponent on a unit in the denominator changes when that unit is written on one line.
Thus L–1 becomes L1 = L in Example 1 at the right.
- Exponents add when the same unit is multiplied by itself.
Thus L × L–1 = L0 = 1 in Example 2 at the right.
The L unit is said to cancel because any number (unit) raised to the 0 power equals 1.