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

Ed, k1ggi k1ggi at arrl.net
Wed Dec 31 22:29:31 UTC 2008

```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

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

```