Editing Conversion of units (section)

=== Checking equations that involve dimensions ===
The factor–label method can also be used on any mathematical equation to check whether or not the dimensional units on the left hand side of the equation are the same as the dimensional units on the right hand side of the equation. Having the same units on both sides of an equation does not ensure that the equation is correct, but having different units on the two sides (when expressed in terms of base units) of an equation implies that the equation is wrong.

For example, check the [[Ideal gas law|universal gas law]] equation of {{nowrap|1=''PV'' = ''nRT''}}, when:
* the pressure ''P'' is in pascals (Pa)
* the volume ''V'' is in cubic metres (m<sup>3</sup>)
* the amount of substance ''n'' is in moles (mol)
* the [[universal gas constant]] ''R'' is 8.3145&nbsp;Pa⋅m<sup>3</sup>/(mol⋅K)
* the temperature ''T'' is in kelvins (K)

<math display="block">\mathrm{Pa{\cdot}m^3} = \frac{\cancel{\mathrm{mol}}}{1} \times
\frac{\mathrm{Pa{\cdot}m^3}}{\cancel{\mathrm{mol}}\ \cancel{\mathrm{K}}} \times \frac{\cancel{\mathrm{K}}}{1}
</math>

As can be seen, when the dimensional units appearing in the numerator and denominator of the equation's right hand side are cancelled out, both sides of the equation have the same dimensional units. Dimensional analysis can be used as a tool to construct equations that relate non-associated physico-chemical properties. The equations may reveal undiscovered or overlooked properties of matter, in the form of left-over dimensions – dimensional adjusters – that can then be assigned physical significance. It is important to point out that such 'mathematical manipulation' is neither without prior precedent, nor without considerable scientific significance. Indeed, the [[Planck constant]], a fundamental physical constant, was 'discovered' as a purely mathematical abstraction or representation that built on the [[Rayleigh–Jeans law]] for preventing the [[ultraviolet catastrophe]]. It was assigned and ascended to its quantum physical significance either in tandem or post mathematical dimensional adjustment – not earlier.