Looking at the answer by mapj, I don't see a "second" 1000 anywhere - it's the same 1000  throughout.  It's assuming that Ztl is 1000.

Each line is of the form: <equation> = <equation with the numbers in> = <simplified version with the bit in brackets calculated> = <result>.

_ quite, and I can't really see what is wrong either, and that's why I put the image up and asked if these were indeed the equations we should be looking at - perhaps the OP has a misprinted older version of the book, or has misread the algebra in some way.

Or indeed there is something else going on and I have not understood the nature of the question at all.

regards Mike.

I noted that, in the clip you posted mapj1  the printing of the triple decimal-exponent separator (1000s separator) is not consistent. For example, no space or comma for'1000' and '7667' but space for '23 000' and '460 000'

I can see from a digital copy of the latest re-print of the 5th Edition, that this has been noticed, but it's still inconsistent, but also there are some typesetting problems, so the bottom and right hand side of each expression appear "clipped':

So, in the above, we see a comma separator for '1,000', no separator for '7667' and a space for '460 0000' and '23 000'.

I have also come to understand that we all see things differently for various reasons, so I do get that this inconsistency could prove a 'bar' to grasping what's going on in the maths. Below is how I think it ought to have been set, which may help some people read it more clearly:

I noted that, in the clip you posted mapj1  the printing of the triple decimal-exponent separator (1000s separator) is not consistent. For example, no space or comma for'1000' and '7667' but space for '23 000' and '460 000'

I can see from a digital copy of the latest re-print of the 5th Edition, that this has been noticed, but it's still inconsistent, but also there are some typesetting problems, so the bottom and right hand side of each expression appear "clipped':

So, in the above, we see a comma separator for '1,000', no separator for '7667' and a space for '460 0000' and '23 000'.

I have also come to understand that we all see things differently for various reasons, so I do get that this inconsistency could prove a 'bar' to grasping what's going on in the maths. Below is how I think it ought to have been set, which may help some people read it more clearly:

It is good that such things are being ironed out - while it's all very well that it iis clear to me in a well lit air conditioned office, (and I already know what the formulae are trying to say, which helps)  I can fully see that for someone in a bit of a hurry who only half remembers the lesson notes from several years ago, perhaps working from a dog eared copy in a badly lit basement or squinting at the online version on a phone screen against the sun, then inconsistent typography is an extra and un-necassary hazard that can lead to k ohms, ohms millohms and so forth being confused.

I must admit to being in 2 minds about the wisdom of  commas though, partly perhaps having worked abroad and with lots of other nationalities, there is the dreaded dot-comma confusion.

Pi= 3,14 ,  1 million is 1.000.000 to the Germans, that kind of thing

Further to those cultural issues, in print or badly rendered computer graphics the comma is not sufficiently different from a stop. It may be age, but to me these  ",  ."   even on this large screen look far too similar.

Perhaps for even more clarity and brevity the use of the international multiplier letter as the decimal marker e.g. 4k7 = 4,700 ohms or 4.7k could be considered  It's what I scrawl over my diagrams already anyway as my writing is too scrappy to be clear otherwise  ;-) 

Anyway thanks for pointing out - funny about the cropping though, I know when I was involved n the 3GPP standards we had a lot of this sort of issue, partly due to submissions using various versions of  MSword, where really a proper publishing program would have been a better choice.

Good that it is being looked at, even if it is not yet quite right in the draft.

Mike