# SI units with more than one prefix in fractions

Is it (in the view of SI) correct to note units with more then one prefix? I discuss this since several months with friends, but we could not find a proper source for our statements yet.

Examples for different notations of an electric field

E1 =  1 MV/m
E2 =  1 kV/mm
E3 = 10 kV/cm

In my research field is no standard established yet so we are continously multiplying.

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I doubt there is a authoritative word on this, but in each sub-discipline there is likely a (or a few) usual practice. – dmckee Nov 12 '12 at 19:36
Be that as it may, science is full of odd (an sometimes incompatible across disciplines) conventions that persist because they have always been that way. Just like the rest of life, really. – dmckee Nov 12 '12 at 19:54

It will probably depend on the exact field you're working in, but this is usually acceptable as long as it is reasonably common in the field and/or it helps clarify the magnitude of the physical quantities involved. For the electric fields you quote, for example, I would choose one or the other depending on the actual distances this field would be sustained across - saying $1\textrm{ kV}/\textrm{mm}$ only makes sense if you're discussing the fields on a millimetre-scale device. On the other hand, I would not be surprised to see the notation $1,000\textrm{ MV}/\textrm{km}$ on a paper discussing atmospheric lightning.

Of course, this notation are not really standard and strictly one should use $10^6\textrm{ V}/\textrm{m}$, but I feel that when they are used it is in the SI spirit of making units as easy to read and make physical sense of while keeping a well-defined, decimal-scale unit system.

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I think calling such notation nonstandard goes a little too far. The prefixes are a fundamental part of the SI specification. – David Z Nov 12 '12 at 23:33
Sure, but you can only push them so far, right? quoting the value of $\hbar$ in kN km pF kV/mA will obscure more than it will help even if it is a formally correct SI unit. On the other hand, giving the value of the solar constant in kWh per day per square metre is not SI but is standard in otherwise-SI engineering disciplines, and with good reason. – Emilio Pisanty Nov 13 '12 at 0:20
@EmilioPisanty the question is not about hours and days, it is about fractions that would cancel out, or melt together. It is like 10^6/10^3 – Jonas Stein Nov 13 '12 at 6:59

The official rule only prohibits the juxtaposition of two or more prefix symbols in the same unit [*]. Therefore your three examples are, so far as I know, allowed.

Personally, I would prefer $E = 1 \cdot \mathrm{MV} \cdot \mathrm{m}^{-1}$, because the (derived or compound) unit for electric field strength is the volt per meter, $\mathrm{V} · \mathrm{m}^{-1}$, and $\mathrm{M}$ is the prefix for this derived unit $1 \cdot 10^6 (\mathrm{V} · \mathrm{m}^{-1}) = 1 \cdot \mathrm{M} (\mathrm{V} · \mathrm{m}^{-1}) = 1 \cdot \mathrm{MV} · \mathrm{m}^{-1}$.

[*] It is 1 mg (one milligram), but not 1 µkg (one microkilogram).

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