Ok, other and maybe more helpful acronyms exist, it probably depends on who taught which set for  O level maths ;-)

edit In the US apparently it is PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction)

But my point is that functional operators like sin cos tan need doing immediately after brackets too - but indices/orders   and functions are sometimes mixed - beware of things like tan^-1 meaning arctan(f), not 1/ (tan(f))

And then of course the sparking favourite of indices within unbalanced units

kA²s

- let through energy

or nVHz^-1/2  

Noise voltage per unit bandwidth - but noting that power, not voltage, scales with bandwidth.

My point was really  that there are dragons to catch  those who do not follow  the rules in order - and I think the OP has been bitten by that.

I also agree the text book could be made clearer.

Mike.

should be dividing the sums by 1000 to convert the values to KΩ?

Not really. 459,000Ω is exactly the same as 459kΩ - mathematically there's no need to divide by 1000. The k prefix itself means x1000.

Strictly speaking, In the metric/SI system the there's only one "unit" for a dimension (in this case Ω for resistance)  Unlike the imperial system where you might divide by 12 to convert between feet and inches, in metric there is only the metre - so really the prefixes are just to 'scale' the number to something more convenient as your write them down (or display them).

   - Andy.

There are always exceptions to the rule.

Whilst it is true that, according to SI units, 1 km² = (1,000m)² = 1,000,000 m², this would lead us to believe that 100,000 A²s ≠ 100 kA²s ... but when reading standards and data sheets of let-through energy of protective devices, you would be a factor of 1000 out if you assumed SI rules are applied ... it seems the "great and the good" of our industry are happy to consider [A²s] as a 'derived unit' and hence use  1 kA²s = 1 k[A²s]

Confused yet?

There are always exceptions to the rule.

Indeed - probably the biggest blunder is that the SI system uses kg rather than g as a base unit for mass (or perhaps that the metric system adopted a unit that was 1000x too small for consistency). If we knew then what we know now things would certainly have been done differently. But for resistance at least it should be fairly straight forward.

   - Andy.

gkenyon said:

hence use  1 kA²s = 1 k[A²s]

Nothing odd about that!

The unit could be Amp-squared-kiloseconds [A² ks].

Note that there should be a space between the different fundamental (or derived) units so the let-through energy is measured in [A² s] or indeed, [s A²] but not [A²s].

It never ceases to amaze me the direction a discussion can head from the original post and I thank all whom have taken their time to contribute. I shall certainly be taking some of this new found knowledge and information with me for future use and knowledge sharing...

I'm very much enjoying the banter and the trip down memory lane all the way from BODMAS to BIDMAS and even PEMDAS, is that really a thing? Who would have thought that there were errors in the SI system. I would have thought that the SI System was as flawless as BS7671 & GN8 ;0)

Did someone actually manage to get Trigonometry into the discussion also? Brilliant :0)

I had a lovely Almond Croissant with a Cappuccino this morning whilst delivering my Tech Talk on the omission of supplementary bonding in a location containing a bath or a shower.

The one thing that I shall definitely take away from this and be putting to good use immediately is what Mapj1 typed 'Measure with a micrometre, cut with an axe' love it :0)

I do appreciate all that has been said, I really do, but I still think that the worked example equations (6.2, 6.3 & 6.4) could be written to give better clarity for everyone at all levels.

We don't need to have a copy of Equation (6.1) at the start of each worked example. The wording above the worked examples eludes to the fact that Equation (6.1) is used.

And then the repeat of the equation, but with the bracketed part worked for us, why?!

I've had a go at re-writing it myself after considering all of the comments and would again appreciate your opinions. I've even managed to chuck a couple of comas in...

How complicated can we make Ohms law look! That's not a challenge BTW ;0)

really its just as valid expressed in joules per ohm of course, then the problem of the meaning of the k being squared or not disappears.

And that has the advantage of really makes it look like a let through  energy as well.. But text books seem frightened by joules for some reason.

I do sometimes wonder if things are written in obscure units so the authors can make something simple look more complex that it is.

Mike.

And that is a version I do fully agree with ;-)  Please don't be put off by the way,

in the manner of 'Look what they've done to my post, ma' as Melanie Safka might have sung, but she didn't, quite.

Discussions on here do sometimes do this sort of thing, and it is ( to me at least) this free flow train of thought stuff that makes it interesting-  all of us learn something, even if it is only what  is not obvious to others and maybe how to better explain it.

Further the most innocent questions are often the best at that...

M
PS the measure with micrometer and axe thing is not originally mine but part of a Hewlett Packard application note, though right now the exact one eludes me. - and it might not actually have been HP..

The original was

Measured with a micrometer

Marked out in chalk

Cut with an Ax.

(A spelling I abhor actually but there we go, they are quite a successful former colony....)

PPS PEDMAS is a thing see here

and it seems that  posters are made to hang up on American classroom walls

Yours for 20 dollars plus postage, laminated I presume

mapj1 said:

really its just as valid expressed in joules per ohm of course, then the problem of the meaning of the k being squared or not disappears.

And that has the advantage of really makes it look like a let through  energy as well.

Agreed - it does look more like energy, but of course it is not energy at all. Joules and Ohms are derived units, so that is probably why A² s is preferred.

1 J = 1 kg m² s‾² and 1 Ω = 1 kg m² s‾³ A‾². Therefore to get to 1 J Ω‾¹ the kg and m cancel out and we are left with A² s.

gkenyon said:

Whilst it is true that, according to SI units, 1 km² = (1,000m)² = 1,000,000 m²,

On reflection, I think that these distances must be the anomaly. Along similar lines, strictly, one square millimetre (1 mm²) should be 1μm². 

Once again, the problem can go away with derived units. So I can fairly easily exert a force of 25 N with my finger tip, which probably has an area of 50 mm². This gives a pressure of 0.5 MPa, which sounds a lot, but is approximately 70 psi.