# Measurement and conversion

Calculations involving measurements such as the length of a beam, the area of a building site, or the volume of a shower recess are expressed in terms of units of measurement such as millimetres, hectares and cubic metres. It is often necessary to convert a given measurement from one unit of measurement to another within a particular system of units (e.g. millimetres to metres in the metric system), or `across' different systems of units (e.g. inches to millimetres).

### Example problem

Suppose a concrete slab is to be laid for a farm shed whose rectangular floor dimensions are $4200$ mm long and $3400$ mm wide. If the slab is to be $110$ mm thick (which is a little more than $4$ inches), how many cubic metres of pre-mixed concrete should be ordered from the supplier? (Other questions that won't be answered here are: if $25$ MPa concrete is to used at a cost of $\$235$per cubic metre including GST, what is the total cost of the concrete? if$10\%$more concrete than the amount calculated using the slab dimensions should be ordered (to account for measurement error or wastage during the pour), what is the new volume required for the order?) Since there are$1000$millimetres in a metre, the slab dimensions expressed in metres are: $4200\text{mm}=\frac{4200}{1000}\text{m}=4.2\text{m};3400\text{mm}=\frac{3400}{1000}\text{m}=3.4\text{m};.$ $110\text{mm}=\frac{110}{1000}\text{m}=0.11\text{m}$ Therefore, the volume of the slab is: $4.2\text{m}×3.4\text{m}×0.11\text{m}\approx 1.58{\text{m}}^{3},$ or$1.58\$ cubic metres.