kA^2s

Just seen your post, Andy.  You've again put it more succinctly than I was going to.  


Yes - the ambiguity will not arise without an exponent (power).


It's implausible that BIPM or IEC intends ambiguities that are resolved only by an apparently unpublished list of which combinations of units and prefixes get treated one way, and which another.


I'm confident the IEC intends to follow the SI system, in its modern form.  And I'm confident that kA2 is intended as equivalent to (kA)2 and nothing else, in that system. But - Graham - you've made me realise that the SI document (I assume you refer also the one I linked in the earlier post?) isn't so clear as we'd like. More examples of what can and can't be done would definitely have been helpful, besides some more use of the word "only". 


As long as we keep to what is explicitly permitted in the SI document, there's not a problem: we get an unambiguous system. 

* Use a prefix on any of the 28 symbols such as A, Pa, W etc (but not kg), on which prefixing is explicitly permitted: page 138, "Prefixes may be used with any of the 29 SI units with special names with the exception of the base unit kilogram". Ok - this doesn't prohibit other use, and "several" non-SI units can also be prefixed (page 145), but there's nothing explicitly permitting a prefix to apply to a longer construction (compound unit) such as a m² or m/s².

* The symbol with its possible prefix is then a single 'thing' to which one can apply an exponent.

* Multiple such 'things' (with or without prefix and with or without exponent) can then be combined by multiplying and dividing. 


For writing, a prefix must attach to its unit without a separator (the examples show no space) and cannot stand alone, and multiplied units must be separated in some way (page 147). This would seem to prevent something like "k A² s" or even k(A² s), although I agree that the space after k would be a sufficient way to make it clear in this case. One reason it would not be a good general principle is that milli and metre have the same letter ... there are several messy features to SI, not least the kg.


Little points: 

"keV is 1000's of eV, NOT 1000s of e multiplied by V."

An electronvolt, eV, is regarded as a unit in itself, albeit only a "non-SI unit accepted for use with SI units" - see Table 8 of the document I linked before. So there's no need to consider the letters e and V separately, any more than the letters in a pascal, Pa.  And even if 'e' were a special separate unit, keV and (ke)V etc would be the same anyway, as there's no exponent to complicate things.

"yet those [spaces] are removed later in Chapter 5"

I haven't found what was meant here.

"DC as a qualifier should not be used to qualify units"

Yes, this is a classic SI strictness, copied into IEC, with the obedience to SI that I would expect. Like the requirement of showing a range "1 V to 3 V" but never "1 - 3 V", it's routinely ignored in practice. The same goes for using a thousands-separator other than a space, as has been done in some examples in this thread (1,000) - not allowed, but many do it. I do wish IEC would follow the SI advice of using a decimal separator that fits the language: decimal commas, while used in many European languages, look strange in English, though I gather they're used in English in South Africa. 

"Units kann be stacked"

I know it's an old convention to combine prefixes, such as the μμF. (Ever seen a capacitance given in cm? Try the CGS system.) But in SI nowadays, combined prefixes aren't allowed - page 143 of the document.  So the kmm² needn't be considered. I assume IEC intends to follow SI (now), not various old conventions.

"k just means times 1000"

Indeed, but the issue is how tightly a prefix "binds" to what comes after it: i.e. the order in which exponents and prefixes should be applied. 

"sulfer with an 'f'":  

I've felt a bit of a comeback of 'sulphur'. But I remember 25 years ago hearing that chemistry students were docked marks for not using the f.

Just seen your post, Andy.  You've again put it more succinctly than I was going to.  


Yes - the ambiguity will not arise without an exponent (power).


It's implausible that BIPM or IEC intends ambiguities that are resolved only by an apparently unpublished list of which combinations of units and prefixes get treated one way, and which another.


I'm confident the IEC intends to follow the SI system, in its modern form.  And I'm confident that kA2 is intended as equivalent to (kA)2 and nothing else, in that system. But - Graham - you've made me realise that the SI document (I assume you refer also the one I linked in the earlier post?) isn't so clear as we'd like. More examples of what can and can't be done would definitely have been helpful, besides some more use of the word "only". 


As long as we keep to what is explicitly permitted in the SI document, there's not a problem: we get an unambiguous system. 

* Use a prefix on any of the 28 symbols such as A, Pa, W etc (but not kg), on which prefixing is explicitly permitted: page 138, "Prefixes may be used with any of the 29 SI units with special names with the exception of the base unit kilogram". Ok - this doesn't prohibit other use, and "several" non-SI units can also be prefixed (page 145), but there's nothing explicitly permitting a prefix to apply to a longer construction (compound unit) such as a m² or m/s².

* The symbol with its possible prefix is then a single 'thing' to which one can apply an exponent.

* Multiple such 'things' (with or without prefix and with or without exponent) can then be combined by multiplying and dividing. 


For writing, a prefix must attach to its unit without a separator (the examples show no space) and cannot stand alone, and multiplied units must be separated in some way (page 147). This would seem to prevent something like "k A² s" or even k(A² s), although I agree that the space after k would be a sufficient way to make it clear in this case. One reason it would not be a good general principle is that milli and metre have the same letter ... there are several messy features to SI, not least the kg.


Little points: 

"keV is 1000's of eV, NOT 1000s of e multiplied by V."

An electronvolt, eV, is regarded as a unit in itself, albeit only a "non-SI unit accepted for use with SI units" - see Table 8 of the document I linked before. So there's no need to consider the letters e and V separately, any more than the letters in a pascal, Pa.  And even if 'e' were a special separate unit, keV and (ke)V etc would be the same anyway, as there's no exponent to complicate things.

"yet those [spaces] are removed later in Chapter 5"

I haven't found what was meant here.

"DC as a qualifier should not be used to qualify units"

Yes, this is a classic SI strictness, copied into IEC, with the obedience to SI that I would expect. Like the requirement of showing a range "1 V to 3 V" but never "1 - 3 V", it's routinely ignored in practice. The same goes for using a thousands-separator other than a space, as has been done in some examples in this thread (1,000) - not allowed, but many do it. I do wish IEC would follow the SI advice of using a decimal separator that fits the language: decimal commas, while used in many European languages, look strange in English, though I gather they're used in English in South Africa. 

"Units kann be stacked"

I know it's an old convention to combine prefixes, such as the μμF. (Ever seen a capacitance given in cm? Try the CGS system.) But in SI nowadays, combined prefixes aren't allowed - page 143 of the document.  So the kmm² needn't be considered. I assume IEC intends to follow SI (now), not various old conventions.

"k just means times 1000"

Indeed, but the issue is how tightly a prefix "binds" to what comes after it: i.e. the order in which exponents and prefixes should be applied. 

"sulfer with an 'f'":  

I've felt a bit of a comeback of 'sulphur'. But I remember 25 years ago hearing that chemistry students were docked marks for not using the f.