Is it possible to have multiple decimal points in a number? Is it ever possible to have multiple decimal points in a number? If so, how?
For example is the value 1.1.2 possible?
This is a question posed purely out of curiosity.
 A: Mathematical notation, like other aspects of human language, is a human creation - we decide what things mean. The system that is most commonly used at the moment is decimal notation:


*

*A "digit" is one of the following integers: $0,1,2,3,4,5,6,7,8,9$.

*If $a_n,\ldots,a_0$ and $b_1,\ldots,b_m$ are digits, and $a_n\neq 0$, then the expression 
$$\Large\color{red}{a_na_{n-1}\,\underset{\substack{\small\strut\,\uparrow\\\small\mathsf{ellipsis}}\,}{{\scriptsize\ldots}}\; a_1a_0\;\underset{\substack{\small\uparrow\,\strut\\\small\mathsf{decimal}\,\\ \small\mathsf{point}\,}}{.}\;b_1b_2\,\underset{\substack{\small\strut\,\uparrow\\\small\mathsf{ellipsis}}\,}{{\scriptsize\ldots}}\; b_m}$$
denotes the number
$$a_n10^n+a_{n-1}10^{n-1}+\cdots+a_110+a_0+b_110^{-1}+\cdots+b_m10^{-m}$$
The purpose of the single decimal point in this notation (ignore the ellipses) is to clarify which parts of the expression correspond to the powers of $10$ where the exponent is $\geq 0$, and those where the exponent is $<0$.  
In this system of notation, there is no meaning of adding a second decimal point. That is not to say that it is impossible to come up with a meaning - perhaps there is some usage in mathematics where a second decimal point would be a convenient and clear way of indicating something, and if there were, perhaps it would then be adopted as a part of our system of notation. But currently, it does not mean anything to write $1.1.2$.
A: The truth is that you can do whatever you want. The point of creating a decimal system and languages for that matter is so that people can have a general framework in which to work and communicate with others. In the decimal system we only use on decimal point. That doesn't mean you can't do whatever you like if it makes you understand it better.
But no, no one uses that because it has no meaning in the decimal system everyone uses nowadays. 
A: IIRC, Babylonian numbers were sometimes written this way,
but their base was 60. 
For example, 3.34.5 might mean
3*3600+34*60+5.
I have a recollection of there being "digits"
to the right of the sexigesimal point,
so that number might mean
3*60 + 34 + 5/60.
A: The "decimal point" is a specific type of "decimal mark", being that it is a dot, period or 'point' that acts as a decimal mark. In other countries, the comma character "," is used as the decimal mark.
A "decimal mark" is a specific type of "radix character", being that it is a radix character for a base-10 number. For a base-2 number, for instance, it might be called the "binary mark", or "binary point".
A "radix character" is a character that separates the integer part of a number from its fractional part in whatever base-notation you are using. Since there are only two parts to this number, there's no need for a further radix character. Since the significance of a digit in a number is defined by its position, things would get very complicated if you allowed the use of multiple radix characters. For instance
1234.56 = 1234.560 = 1234.5600

But does
1234.56 = 1234.56. = 1234.56.0 = 1234.560. = 1234.560.0

?
Since the position of a number in a multi-radix-character notiation system can now be determined with respect to multple points, it would be hard to definitively parse a number, which would kind of defeat the point of a notation system.
A: As far as I know, nobody uses such notations. For example, if you interpret $1.2.3$ as $(1.2).3=\left(1+2\cdot 10^{-1}\right)+3\cdot10^{-1}=1.5$ or as $1.(2.3)=1+\left(2+3\cdot 10^{-1}\right)=3.3$
Of course, what I just wrote isn't useful. To use such symbols, you must define them first and see if they have any use in mathematics maybe in a totally ordered field where you have three types of elements not two types like $\mathbb{R}$ (positive and negative numbers).
A: In software engineering it's very common to use 2 or 3 'decimal points' to provide information about the version of an application.
For example the version of Skype I have installed is '5.10.32.116'. 
For more details see Software versioning on Wikipedia.
Also if you look at the very bottom of this page you should notice the revision number e.g. 'rev 2013.7.8.823' which uses decimal points to divide the information to easily readable chunks.
A: I think in the notation it is written, this is ambiguous. In a decimal system, a.b = a + b*(a/10), where .=decimal point.
So if you interpret 1.1.2 as 1.(1.2), this is 1 + (1/10)*1.2 = 1 + 0.12 = 1.12. However if 1.1.2 means (1.1).2 then it is 1.1 + (1.1/10)*2 = 1.1 + 0.22 = 1.32.
A: We could if we only decide to ! (even an infinity in this $10$ protuberances alien notation :-))
$$\pi=3.7.15.1.292.1.1.1.2.1.3.1.14...$$
$$e=2.1.2.1.1.4.1.1.6.1.1.8.1.1.10...$$
$$\phi=1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1...$$
$$171/372=0.2.5.1.2.3$$
A: I'm surprised no one has mentioned this yet.
The answer is Yes. Case in point: IP addresses. Example: 192.168.1.1
:)
A: Think about time in hours, minutes and seconds - 8:12:56 - that is a form which uses a double separator.
The point is not whether it can be done, but when it is useful and coherent to do it.
A: It is of course possible to define whatever you like.
Hewlett-Packard defined an interesting and very handy interpretation of two decimal points for some of their later calculators, starting with the HP-32SII.
If I enter 1.2, I see 1.2.  If I enter 1.2. I see 1 2/.  Now if go on with 1.2.3, I see 1 2/3.  It interprets a number with two decimal points as a fraction, with the three numbers being the whole part, the numerator, and the denominator.
When I hit ENTER, I get 1.66666666667, where it gives me the resulting approximate decimal value.
I love this handy use of two decimal points.  I use it all the time.
A: Some calculators, like the latest HP ones, accept a number with two decimal points as a fraction.  Typing $a.b.c$ gives $a \frac bc$.  
Another use for multiple radices is where 'the point of conversion' is different to the quoted unit.  It's easier to do with weights annd measures, than with number.  For example, there are $1440$ minutes in a day.  The conversion of this into duodecimal, would take to account that the preferred division of the day would be $12$ hours of $144$ minutes.
One could write this $1440$ as $144;0.$, where the conversion actually takes place at the semicolon, but the radix is placed at the point (in both cases).  So $1.$ minite is converted as $;1.$, gives $;1.2497\dots$ minutes. 
One could use mutiple radices to demonstrate conversion of metres to millimetres, or similar in a like fashion.  eg  1;000. metres (;) = 1;000. millimetres (.).  
Added fractions are fractions with continued numerators, for example the following.  They arise quite naturally out of the old measure, eg feet, inches and eights would be $f \frac i{12} \frac e8$.  $$a \frac bc \frac de = a \frac {b\frac de}c$$
They're also pretty nifty for added fractions, where one might use several bars to represent radices at spaced units.  For example, amounts of monye (in £sd), could be written as  $$£l/s/d\frac f4 =  l \frac s{20} \frac d{12} \frac f4$$
One then uses vertical bars as the radix of several units (eg pounds and pence), to rearrange the units, while still keeping the $240$ pence in the pound ratio, eg these South-german currencies, derived from the frankish pound.
$$ l \mid \frac s{20} \frac d{12} \mid \frac f{4} = l \mid \frac {xr}{60} \frac d{4} \mid \frac f4$$
One sees that the product of the denominators is the ratio of the units, must remain the same, but intermediate units can be reorganised.  The bars represent the radix or unitpoint for the pound and penny.  There are still 240 pence in the pound, but the shilling (12d) is being replaced by kreuzer or groat (4d).  Once this rearrangement occurs, one could then rearrange the groat of 16 fathings, from an intermediate unit of a penny of four fathings, to a heller of two fathings.  
But in the main, there is really little end to having mutlople radices.
