[time-nuts] Need schoolin PPM vs E to the umth?

[WB6BNQ]

Ed,

I think your Email was right on point and should not annoy anyone.  It is most
helpful to point out inconsistencies of a common nature.

I also have missused the "E" notation in exactly the way you discussed without
ever giving it a thought.  Now I will be constantly checking myself.

Bill....WB6BNQ


"Ed, k1ggi" wrote:

> Chris -
>
> To help avoid too much confusion, it needs to be pointed out that this 'E'
> notation gets used somewhat imprecisely in context, and you have to read
> "what they meant" rather than "what they wrote".
>
> In the convention of scientific E notation, Eb (sometimes eb) denotes a
> factor whose value is 10 raised to the power b.
>
> see
> http://en.wikipedia.org/wiki/Scientific_notation
>
> (This has nothing to do with that mathematical 'e' that gets raised to all
> sorts of powers in electronics, etc. -- eb does not mean 2.718... raised to
> the power b.)
>
> Examples:
> 3E2 = 3E+2 = 300, a number with two factors, the first being three and the
> second being 10 to the power of positive two, or 100.
> 8E2 = 800
> 9E2 = 900
> 10E2 = 1000
> 1E2 = 100
> 10E1 = 100
> Calculators such as Excel or Google deal with this notation.
> No explicit symbol for a multiplication operator appears within the notation
> itself, it is understood.
>
> Compare this to caret notation, where
> a^b denotes a raised to the power b.
> 3^2 = 9
> 10^2 = 100
> 3*10^2 = 300
> And just for illustration,
> e^-1 = 0.36... where this _is_ the 'other' e thing, 2.718....
> Calculators also understand this notation.
>
> Now, the values of 10^2 and 10E2 differ by a factor of 10.
> 3*10^2 = 300
> 3*10E2 = 3000
> 3*1E3 = 3000
> 3E3 = 3000
>
> So here's the thing. When you read about 1 part in 10^2 or 1 part in 10E2,
> you find that the writers quite often really meant the same thing,
> regardless of the numbers being different, and you have to make a mental
> adjustment.
>
> On this list, where precision and accuracy are so highly regarded, this bit
> of ambiguity is accommodated, but if you're not paying attention, a
> calculation can be off by a factor of 10. Used equipment also gets described
> this way when somebody has to type it up, so it pays to check original
> manufacturer's specs.
>
> With some savvy, it's a good bet that when you see a leading 10, i.e.
> 10Eanything, the writer meant to convey only the general notion of the
> exponent, not the actual numeric value of the expression. This is because if
> the actual value were intended, it would have been written as, say, 1E3
> rather than 10E2. OTOH, any leading number other than 10, as in 9E2, doesn't
> readily lend itself to misinterpretation. 10E2 literally means 1000, but may
> need to be read as 100, whereas 9E2 always means 900. You would think that
> if something goes from 9 to 10 it would come out bigger, but it doesn't.
> See?
>
> <snip>
> >an oscillator that is accurate to 1%, is accurate to one part in 100, or
> >expressed in scientific notation, 1 part per 10E2.
> <snip>
>
> 10E2 is a number. If you put 1 over 10E2 into a calculator, it doesn't come
> out 1%, it comes out 0.1%, 10 times smaller, but here the context reveals
> the intent, so there you go. Intent is harder to figure out when there are a
> dozen zeros floating around and there is less explanatory context.
>
> So just be on guard when you see 10Eanything, check for reasonableness, and
> consider embracing 1Eanything, which is unambiguous.
>
> Not intending to drive anyone nuts,
> Ed, k1ggi
>
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