Limitations
The factor-label method can convert only unit quantities for which the units are in a linear relationship intersecting at 0. Most units fit this paradigm. An example for which it cannot be used is the conversion between degrees Celsius and kelvins (or Fahrenheit). Between degrees Celsius and kelvins, there is a constant difference rather than a constant ratio, while between Celsius and Fahrenheit there is both a constant difference and a constant ratio. Instead of multiplying the given quantity by a single conversion factor to obtain the converted quantity, it is more logical to think of the original quantity being divided by its unit, being added or subtracted by the constant difference, and the entire operation being multiplied by the new unit. Mathematically, this is an affine transform, not a linear transform . Formally, one starts with a displacement (in some units) from one point, and ends with a displacement (in some other units) from some other point.
For instance, the freezing point of water is 0° in Celsius and 32° in Fahrenheit, and a 5° change in Celsius correspond to a 9° change in Fahrenheit. Thus to convert from Fahrenheit to Celsius one subtracts 32° (displacement from one point), multiplies by 5 and divides by 9 (scales by the ratio of units), and adds 0 (displacement from new point). Reversing this yields the formula for Celsius; one could have started with the equivalence between 100° Celsius and 212° Fahrenheit, though this would yield the same formula at the end.
To convert Celsius to Fahrenheit, simply plug in the known numbers in the above formula.
To convert Fahrenheit to Celsius, plug the known temperature into the above formula.
EX. °F = 1.8(-40°C) + 32° = -40°F (Identical temperature point in °C and °F)
EX. °C = (98.6°F-32°) ÷ 1.8 = 37°C (Known standard body temperature in °C and °F)
Read more about this topic: Units Conversion By Factor-label
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