What does E mean in 9.0122222900391E-5?

Question

I often find this at the bottom of pages.

Page generated in 0.00013899803161621

Sometimes, I come across

Page generated in 9.0122222900391E-5

What does that time mean?

I tried searching Wikipedia for E and maths but found the e mathematical constant. My guess is E stand for Exponential and -5 is the power it is raised to. And the displayed time is a really small number. But that doesn't make sense when compared to the other time in the question. 0.00013899803161621 is bigger than 9.0122222900391E-5.

If it means x times $10^{-5}$, then 9.0122222900391E-5 will be 0.000090122222900391 which is smaller than 0.00013899803161621. What does E stand for?

In case anyone knows: where is this particular number coming from? There are a large number of google hits for it, many of which are not mirrors of this site, whereas (unsurprisingly) if I change the last decimal place by 1 in either direction there are no hits at all. — Michael Lugo, Aug 25 '11 at 23:21
@Michael, for whatever it's worth it is the multiple of $10^{-18}$ that is closest to $189\times 2^{-21}$. Google also knows various multiples of $2^{-22}$ to a similar precision. They all seem to be values related to timing. Possibly related, I have come across a bug in some versions of Linux whereby the system time would be off by exact multiples of $\frac{2^{42}}{10^{9}}$ seconds. Notice that $42+22=64$... — hmakholm left over Monica, Nov 12 '11 at 20:37
So it is really a computer question, not a math question. If you want something other than wild speculation to the supplementary question "what does the E stand for?" you should try a computer site... — GEdgar, May 08 '12 at 12:00
I agree with @GEdgar. It's not a math question. So I suggest to delete it (or something similar). — vesszabo, Jul 18 '17 at 20:46
How did it get so many views? It was linked from somewhere else...somewhere with lots of users. — GEdgar, Jul 18 '17 at 21:56

score 72 · Accepted Answer · edited Jul 03 '17 at 00:59

72

It means $9.0122222900391\times 10^{-5}$. This is known as "scientific notation".

edited Jul 03 '17 at 00:59

K Split X

6,565

answered Oct 07 '10 at 16:22

Hans Lundmark

53,395

2

Is the E an abbreviation for something? – Rasmus Oct 07 '10 at 16:29
10

On calculators that E is sometimes denoted "exp", which is short for "exponential". In fact, "exponential notation" is another name for "scientific notation" – Andy Oct 07 '10 at 16:33
This probably explain the "abuse" of $\log=\log_10$. :) – AD - Stop Putin - Oct 07 '10 at 16:54
3

Well, only mathematicians the following is true: "Thou shalt not have another base before e", right? ;) – Andy Oct 07 '10 at 16:59
The reason for using this notation is it lets you represent very large or small numbers more compactly. For instance, writing 6.26068E-34 is much more convenient than 0.000000000000000000000000000000000626068, and easier to get an idea of its size without counting 33 zeros. – Nate Eldredge Oct 07 '10 at 20:06
13

@AD.: I was really confused for a while, until I realized that you meant $\log_{10}$ rather than $\log_1 0$. :-) – Hans Lundmark Oct 08 '10 at 11:28
@Andy The 11th commandment! – AD - Stop Putin - Oct 09 '10 at 04:41
2

@Hans Lundmark: Of course, sorry :) – AD - Stop Putin - Oct 09 '10 at 04:41
so eN or e(N) always means 10^N or 10^(N)?? – oldboy Nov 18 '18 at 20:45

score 17 · Answer 2 · answered Oct 07 '10 at 16:23

17

E-5 just means x 10^(-5) i.e. divided by 100000

answered Oct 07 '10 at 16:23

Chris Card

1,988

if -5 is positive, it's multiplication? it's only division when -5 is a negative like -5?? – oldboy Nov 18 '18 at 20:46
Yes, that's correct. – Toby Mak Sep 12 '19 at 12:35

score 8 · Answer 3 · answered Jan 17 '12 at 23:39

8

I have always taken the E or e to mean "exponent of 10." This construction parses in all modern computing languages as an IEEE754 double or single precision number.

answered Jan 17 '12 at 23:39

ncmathsadist

49,383

What does E mean in 9.0122222900391E-5?

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