For instance, I have the following problem:
convert:
$\frac{{m^2}^{\circ}C}{W}$ to $\frac{ ^{\circ} F * ft^{2} * hr}{Btu}$
Take $x \frac{{m^2}^{\circ}C}{W}$ for instance, how would I convert it to $y \frac{{m^2}^{\circ}F}{W}$? The reason that I am confused is that there is no conversion factor, to my knowledge, that I can multiply x by to get y.
On
Notice, The temperature scales in $^\circ C$ & $^\circ F$ are co-related as follows $$\frac{^\circ F-32}{9}=\frac{^\circ C}{5}\implies ^\circ F=\frac{9({^\circ}C)+160}{5}$$
Hence, we can convert from $x\frac{m^2 {^\circ}C}{W}$ to $y\frac{m^2 {^\circ}F}{W}$ as follows $$\color{red}{y}=\color{red}{\left(\frac{9x+160}{5}\right)}\ \ \color{blue}{\frac{m^2 \ {^\circ}F}{W}}$$
Use just the stretching factor I suppose.
$^\circ C$ and $^\circ F$ are used for a temperature range in this formulas.
So just use $5/9$ or $9/5$ without any shift.