I'm trying to figure out the preferred way to write unit expressions and division is causing me some confusion. I'm aware of the negative exponent notation, but here I'm looking for a solution using the division sign (solidus).
The SI unit standard states that we should write "(a/b)/c, not a/b/c" (http://physics.nist.gov/Pubs/SP330/sp330.pdf), which makes sense. However (a/b)/c could also be expressed as a/(b·c). I have seen that in some cases for example mi/(h·s). The base unit for Volt = kg·m^2/(s^3·A^1) also follows this style as seen here: http://physics.nist.gov/cuu/Units/checklist.html. That pages also notes that "The solidus must not be repeated on the same line unless parentheses are used."
The only consistent rule I can come up with is that only one solidus should be allowed. That would mean kg·m^2/(s^3·A^1), mi/(h·s) and a/(b·c) are correct, but it does go against what the SI standard suggests with (a/b)/c.
So what do you think?
The intention of the standard is probably just that a/b/c should not be used, because it could be seen as ambiguous, not that (a/b)/c should never be written as a/(b·c).
ISO 80000-1:2009 has an example on page 23 expressing precisely this, saying
And by using negative exponents in units, the "problem" can of course be completely avoided, as you say: V = kg·m²·s⁻³·A⁻¹.