Unit Factor Method
Convert between units with the unit factor or factorlabel method
Unit Factor Method
Unit converting from one system to an other can be done with the unit factor method  also called dimensional analysis.
The relationship between two different units can be expressed as
$$ 1 (u_1) = x (u_2) \tag{1} $$
where
u_{1} = unit 1
u_{2} = unit 2
x = converting factor from u_{2} to u_{1}
Example  inches vs. mm
$$ 1 (in) = 25.4 (mm) $$
Dividing the relationship (1) with the two sides  two unit factors for the relationship can be expressed as
$$ \frac {1 (u_1) }{ x (u_2)} = 1 \tag{2} $$
$$ \frac {x (u_2) }{ 1 (u_1)} = 1 \tag{3} $$
Example  inches vs. mm
$$ \frac {1 (in) }{ 25.4 (mm)} = 1 $$
$$ \frac {25.4 (mm) }{ 1 (in)} = 1 $$
Converting a value from one unit to an other can then simply by done by multiplying both sides of eq. 2 or 3 with the value.
$$ \frac {1 (u_1) \ a (u_2)}{ x (u_2)} = a (u_2) \tag{2a} $$
$$ \frac {x (u_2) \ b (u_1)}{ 1 (u_1)} = b (u_1) \tag{3a} $$
Example  Converting 10 mm to inches
$$ \frac {1 (in) \ 10 (mm)}{ 25.4 (mm)} = 10 (mm) $$
$$ 0.39 (in) = 10 (mm) $$
Factorlabel Method
The factorlabel method is an sequential combination of conversion factors where numerator and denominator of the conversion factor fractions can be cancelled out to achieve a desired set of dimensional units.
$$ \frac {1 (u_1) }{ x (u_2)} \ \frac {y (u_2) }{ 1 (u_3)} \ \frac {1 (u_3) }{ z (u_4)} = \frac {y (u_1) }{ x z (u_4)} \tag{4} $$
Example  Converting 2.5 feet to mm
Th unit factor for mm to feet can be calculated using eq. 4 as:
$$ \frac {25.4 (mm) }{ 1 (in)} \ \frac {12 (in) }{ 1 (ft)} = 304.8 (\frac {mm}{ft}) $$
10 mm can be converted to feet as
$$ 308.5 (mm/ft) \ 2.5 (ft) = \underline{771.3} (mm) $$
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