Apart from the Tamil fractions and numerals there are other miscellaneous symbols. These can be typeset in XeLaTex or LuaLaTeX. Make sure you have installed the Noto Sans Tamil Supplement Font. To insert the Unicode character say in TeX studio press CTRL+ALT+u and input the Unicode number in the dialog box and press enter. i will mention the Unicode block and its corresponding character.  Whenever we can type the symbols in IBus [uses the Tamil99 layout] I'll mention the  keystrokes in the first column.Measures of grain 
 11FD5    ЁС┐Х   1 роиெро▓்     one grain of paddy
11FD6    ЁС┐Ц   роЪெро╡ிроЯ்роЯு   360 grains of paddy
11FD7    ЁС┐Ч    роЖро┤ாроХ்роХு  1,800 grains of paddy
11FD8    ЁС┐Ш    роЙро┤роХ்роХு    3,600 grains of paddy
-        роЙро░ி   2 роЙро┤роХ்роХு  7,200 grains of paddy
11FD9    ЁС┐Щ   рооூро╡ுро┤роХ்роХு  10,800 grains of paddy
0BF3     ௳    рокроЯி        14,400 grains of paddy 
11FDA    ЁС┐Ъ    роХுро░ுройி*    115,200 grains of paddy
11FDB    ЁС┐Ы   рокродроХ்роХு     230,400 grains of paddy
11FDC    ЁС┐Ь   рооுроХ்роХுро░ுройி*  345,600 grains of paddy
* рооро░роХ்роХாро▓் роОрой்ро▒ுроо் роЕро┤ைроХ்роХро▓ாроо் 
* can also be called Marakkaal
Old currency symbols 
11FDD    ЁС┐Э    роХாроЪு        Paise
11FDE    ЁС┐Ю    рокрогроо்      Money
11FDF    ЁС┐Я    рокொрой்     Gold coin
11FE0    ЁС┐а    ро╡ро░ாроХрой்    Gold coin bearing boar insgignia
 
Symbols of weight, length, and area 
11FE1    ЁС┐б    рокாро░роо்     Equals approx 227 kg
11FE2    ЁС┐в    роХுро┤ி*     Approx 121 sq ft
11FE3    ЁС┐г    ро╡ேро▓ி     Approx 242,000 sq ft
 Agricultural symbols          
11FE4    ЁС┐д    роирой்роЪெроп்    Wet Cultivation
11FE5    ЁС┐е    рокுрой்роЪெроп்    Dry Cultivation
11FE6    ЁС┐ж    роиிро▓роо்       Land
11FE7    ЁС┐з    роЙрок்рокро│роо்    Salt Pan
 
Clerical symbols   
 11FE8    ЁС┐и    ро╡ро░ро╡ு        Credit
11FE9    ЁС┐й     роОрог்        Number
11FEA    ЁС┐к    роиாро│родு       Current date sign
11FEB    ЁС┐л    роЪிро▓்ро▓ро░ை     Change 11FEC    ЁС┐м    рокோроХ         Spent sign
11FED    ЁС┐н    роЖроХ         Total Sign
 
Other symbols and abbreviations  
11FEE    ЁС┐о    ро╡роЪроо்        Posession
11FF0    ЁС┐░    рооுродро▓ிроп      et cetera
11FF1    ЁС┐▒    ро╡роХைропро░ா   indicates items of a family or kind 
11FFF    ЁС┐┐    -            End of Text
 
Symbols in the Standard Tamil Unicode Block 
A    0BF3    ௳    Day also pillaiyar suli  роиாро│்
X    0BF4    ௴    Month                   рооாродроо் 
C    0BF5    ௵  Year                    ро╡ро░ுроЯроо்
V    0BF6    ௶    Debit                   рокро▒்ро▒ு
B    0BF7    ௷   Credit                  ро╡ро░ро╡ு
D    0BF8    ௸  As Above                 рооேро▒்рокроЯி
A    0BF9    ௹    Rupee                   ро░ுрокாроп்  
S    0BFA    ௺    Number          роОрог், роиிро▓ுро╡ை
N    0BD0    рпР    Om                        -
L    0BF1    ௱    Raja                   ро░ாроЬ  
 
Some Special Symbols
G        ЁЯМХ       Full Moon    рокро╡ுро░்рогрооி
H        ЁЯМС       New Moon     роЕрооாро╡ாроЪை
J        ★       Karthigai    роХாро░்род்родிроХை
^$       ₹        Rupee        ро░ூрокாроп்   
To typeset the above symbols the following packages are needed they are 
- lmodern
 - MnSymbol
 - wasysym
 - tfrupee
 - marvosym [has some other common symbols]
 
The full moon ,new moon and the star needs to be in math mode.Here is an MWE
\RequirePackage[orthodox]{nag}
\documentclass[a4paper,12pt]{article}
\usepackage{fontspec}
\usepackage[T1,TS1,OT1,OT4,TU,EU1,QX,T5,LY1]{fontenc}
\usepackage[stretch=10]{microtype}
\setmainfont{Times New Roman}
\usepackage{lmodern}
\usepackage{marvosym}
\usepackage[cmsy]{MnSymbol}
\usepackage{wasysym}
\usepackage{tfrupee}
\begin{document}  
     $\newmoon \fullmoon $ 
    \rupee $\filledlargestar$
\end{document}  
   
 
 
* Different Authorities give different measure for kuli. 
Most of these symbols are not in current use.
Some Measurement are still used in oral form.   
Some Symbols are used only for official documents although it has become rare nowadays. 
Shriramana Sharma and others have done a huge work to make sure Tamil numbering and measuring system were included in Unicode. Also Shriramana Sharma is the author of the font Lohit Tamil Chart Font.Kudos to them for their hard work.   
 
 
Reference