Updating syntax to makes things clear and reduce confusion

Improving the syntax of my formulas.  Changed variable names to make the fact that these are scaling by unit named.

Functions:

$$h=\frac{s_{\text{length}}\cdot s_{\text{mass}}}{c}$$

$$\stackrel{<span\; style="background-color:\; white;"><span\; style="color:\; black;">ˉ</span></span>}{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">h</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;">=</span></span>\frac{{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">length</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;">\cdot </span></span>{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">mass</span></span>}}}{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">2</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">\pi </span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">c</span></span>}}$$

$$\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">G</span></span>}<span\; style="background-color:\; white;"><span\; style="color:\; black;">=</span></span>\frac{{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">length</span></span>}}}{{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">mass</span></span>}}}$$

$${\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">k</span></span>}}_{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">B</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;">=</span></span>\frac{{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">length</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;">\cdot </span></span>{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">mass</span></span>}}}{{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">temp</span></span>}}}$$

$${\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">ϵ</span></span>}}_{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">0</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;">=</span></span>\frac{{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">charge</span></span>}}^{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">2</span></span>}}}{{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">length</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;">\cdot </span></span>{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">mass</span></span>}}}$$

Unit Scaling:

$${\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black;">length</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">3.64117228161056598231271787236294544974398351386800</span></span>}<span\; style="background-color:\; white;"><span\; style="color:\; black;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">1</span></span>}{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">0</span></span>}}^{<span\; style="background-color:\; white;"><span\; style="color:\; black;">-</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;">18</span></span>}}\text{<span style="background-color: white;"><span style="color: black;"> m</span></span>}$$

$${\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black; font-size: xx-small;">mass</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">5.45551186133462083261573179563841219265538485514280</span></span>}<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">1</span></span>}{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">0</span></span>}}^{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">-</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">8</span></span>}}\text{<span style="background-color: white;"><span style="color: black; font-size: xx-small;"> kg</span></span>}$$

$${\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black; font-size: xx-small;">temp</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">1.43877687750393380214667160154391159519906942314810</span></span>}<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">1</span></span>}{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">0</span></span>}}^{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">-</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">2</span></span>}}{\text{<span style="background-color: white;"><span style="color: black; font-size: xx-small;"> K</span></span>}}^{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">-</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">1</span></span>}}$$

$${\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">s</span></span>}}_{\text{<span style="background-color: white;"><span style="color: black; font-size: xx-small;">charge</span></span>}}<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">1.32621132205611059057563089920041186351594040760120</span></span>}<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">1</span></span>}{\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">0</span></span>}}^{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">-</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="color:\; black;\; font-size:\; xx-small;">18</span></span>}}\text{<span style="background-color: white;"><span style="color: black; font-size: xx-small;"> C</span></span>}$$