Editing Conversion of units (section)

=== Example ===
Starting with:
: <math>Z = n_i \times [Z]_i</math>
replace the original unit {{tmath|1= [Z]_i }} with its meaning in terms of the desired unit {{tmath|1= [Z]_j }}, e.g. if {{tmath|1= [Z]_i = c_{ij} \times [Z]_j }}, then:
: <math>Z = n_i \times (c_{ij} \times [Z]_j) = (n_i \times c_{ij}) \times [Z]_j</math>

Now {{tmath|1= n_i }} and {{tmath|1= c_{ij} }} are both numerical values, so just calculate their product.

Or, which is just mathematically the same thing, multiply ''Z'' by unity, the product is still ''Z'':
: <math>Z = n_i \times [Z]_i \times ( c_{ij} \times [Z]_j/[Z]_i )</math>

For example, you have an expression for a physical value ''Z'' involving the unit ''feet per second'' ({{tmath|1= [Z]_i }}) and you want it in terms of the unit ''miles per hour'' ({{tmath|1= [Z]_j }}):

{{ordered list
|1= Find facts relating the original unit to the desired unit:
: 1 mile = 5280 feet and 1 hour = 3600 seconds

|2= Next use the above equations to construct a fraction that has a value of unity and that contains units such that, when it is multiplied with the original physical value, will cancel the original units:
: <math>1 = \frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}}\quad \mathrm{and}\quad 1 = \frac{3600\,\mathrm{s}}{1\,\mathrm{h}}</math>

|3= Last, multiply the original expression of the physical value by the fraction, called a ''conversion factor'', to obtain the same physical value expressed in terms of a different unit. Note: since valid conversion factors are [[dimensionless]] and have a numerical value of [[one]], multiplying any physical quantity by such a conversion factor (which is 1) does not change that physical quantity.
: <math> 52.8\,\frac{\mathrm{ft}}{\mathrm{s}} =
 52.8\,\frac{\mathrm{ft}}{\mathrm{s}}
 \frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}}
 \frac{3600\,\mathrm{s}}{1\,\mathrm{h}} =
 \frac {52.8 \times 3600}{5280}\,\mathrm{mi/h}
 = 36\,\mathrm{mi/h}</math>
}}

Or as an example using the metric system, you have a value of fuel economy in the unit ''litres per 100 kilometres'' and you want it in terms of the unit ''microlitres per metre'':
: <math> \mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}} =
 \mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}}
 \mathrm{\frac{1000000\,\rm{\mu L}}{1\,\rm{L}}}
 \mathrm{\frac{1\,\rm{km}}{1000\,\rm{m}}} =
 \frac {9 \times 1000000}{100 \times 1000}\,\mathrm{\mu L/m} =
 90\,\mathrm{\mu L/m}</math>