Do some scientists create equation that arent based on si units.

any equation's variables can be converted from one unit to another; no equation is "meant to use a different set" but can be written in another way. In most physics textbooks only SI units are used.

 

In certain cases equations might be simpler in some particular system of units. A particularly famous one is that where the units are such that all the fundamental constants (Planck's constant, speed of light, gravitational constant) equal 1 and simply omitted from the equations. These units, however, are completely unsuitable for practical use. A more practical example is the Gaussian units, which partially overlap with SI. In these units, equations of electrodynamics are somewhat simpler, so many texts use them. In non-relativistic classical mechanics equations are usually independent of the choice of units.

In any case, anyone using any equation ought to mention assumptions on the units.

 

People use non-SI units every day. Classic example would the fuel consumption of your car being specified in miles per gallon.

However you should never assume any particular units have been used. Always check and recheck..

http://en.wikipedia.org/wiki/Mars_Climate_Orbiter

 

In some fields of work it's vey inconvenient to use SI base units such as the meter. Astronomers frequently work in "light years" for example.

 

What I hear from some friendly astronomers is that light-years as a distance unit has a ring of SciFi affection to it. Parsec is perceived as the more appropriate unit.