Maths for Diploma Studies

Without units, communicating the measurement of something is impossible. Over the years, we have evolved from using barley grains arranged end to end to measure shoe size to having a definitive official kilogram stored in a vault in France against which all kilograms on earth are measured. In this section, we will list and explain the units of measurement used in CIBD lessons and how we use them.

System International (SI) units

At the CIBD, we use the SI system for our measurement units wherever possible. The table below shows the SI units you will encounter.

Table: SI units

Some units are derived from base units. In order to cancel them, we need to convert them to their base unit. The table below shows the ones you may encounter in Diploma lessons along with their base units.

Table: Derived SI units

Unit representation

We learned earlier that units can be written as fractions or as indices. For working with units in unit conversion and unit cancellation, it is easiest to show units as fractions. To convert between the two forms, you need to remember that x^-1 is the same as 1/x, so J/kg is the same as J.kg^-1. When the unit already has an exponent that is used in place of the 1. For example, in density kg/m³ we write it as kg,m^-3. As with rates, the horizontal or diagonal line means per. So kg/m³ is kilograms per cubic metre. The ^{-1 -2} or ^-3 also represent the word per.

Table: Three representations of commonly used units

Reciprocals effect on units

When we take a reciprocal of a number, its unit becomes inverted. For example, if we take a reciprocal of a heat transfer coefficient, the units change from:

To:

Now we know our units and how they can be represented, we can start to make use of them. We do that next in unit conversion and cancellation.