8
$\begingroup$

I am doing an optics simulation involving transmission and reflection coefficients very close to 1, such as 0.999. While I was an undergraduate student, a professor mentioned that, in certain fields, people characterise such numbers by the number of '9's after the dot. I tried to find any mention of this on the internet, and a name for that number of '9's, but didn't find anything.

Could anyone point me in the right direction?

Incidentally,

  1. The formula for that number of '9's in the number x is -log_10(1-x).
  2. This might well be an engineering question.
  3. ChatGPT suggests that that number of '9's is called 'nines'. Makes some sense, but the rest of the internet seems to be agnostic to this term.
Improve this question
$\endgroup$
11
  • 5
    $\begingroup$ I’m voting to close this question because it is not about physics. $\endgroup$
    – Vincent Thacker
    Commented Jun 5 at 10:15
  • 6
    $\begingroup$ This type of figure is used in system availability specifications. en.wikipedia.org/wiki/High_availability#Percentage_calculation $\endgroup$
    – Mark H
    Commented Jun 5 at 10:26
  • 1
    $\begingroup$ @MarkH, so it is called 'nines', at least in system availability specs. Thanks, very helpful. $\endgroup$
    – jcuk
    Commented Jun 5 at 10:30
  • 6
    $\begingroup$ This is a question about standard terminology used in experimental physics research. I wouldn't close it. $\endgroup$
    – user34722
    Commented Jun 5 at 11:07
  • 1
    $\begingroup$ @VincentThacker Note that points 1 and 3 mention notation and terminology, while point 2 mentions notation only. (This question is about terminology, not notation.) $\endgroup$
    – Sten
    Commented Jun 5 at 14:53

1 Answer 1

Reset to default
13
$\begingroup$

I've heard 'nines' used frequently in quoting the purity of a material, and it turns out that this is a standard, though informal term. Wikipedia has this to say:

"Nines are an informal logarithmic notation for proportions very near to one or, equivalently, percentages very near 100%."

It apparently also comes up commonly in purity of industrial gases and system up-time in computer services. Mathematician Terence Tao proposed it as a measure of risk here (this is where I first heard it named).

However the most relevant and standard unit to use in these cases is probably to quote one minus your quantity of interest in dB (decibels). This is the standard way of quoting loss, transmission and reflection coefficients of optical and microwave components, and is much more common than nines. It also maps one-to-one with nines:

0.9 transmission: -10 dB loss

0.99 transmission: -20 dB loss

Etc.

Improve this answer
$\endgroup$
1

Not the answer you're looking for? Browse other questions tagged or ask your own question.