Different numeration on banknotes

It seems that the oldest numeration on banknotes was sequence of letters followed by sequence of numerals. Here is one of the examples 100 years old

(Source: https://t.me/s/enjoyyourcollection?q=SWEDEN+1918 )
It is from Sweden and the style of letters use in different cases: upper and lower.

There is an outstanding example of such numbering during the dissolution of the USSR. One of its territories decided to add numbers on a common printer!
 

(Source: https://t.me/s/enjoyyourcollection?q=uzbekistan+1993 )

Look at the number:

it consists of the dots from matrix printers! It should be very hard work, printers especially dot matrix ones worked very unstable those days.  And again the case (upper or lower) of letters  was essential for the series.

But the numeration of one more style, a fraction in front of the number, was introduced in XX century. As far as I know, here is one of oldest example of it

(Source: https://www.delcampe.net/en_US/collectibles/coins-banknotes/banknotes/south-africa/ship-1928-1947-south-africa-10-shillings-1940-rarity-just-published-low-start-no-reserve-1655786861.html )

Known to me style there is the use of capital letter at the top (nominator of the fraction) and number at the bottom. 

 Of course some languages do not have capital letters, so just a letter was used, and a territory of the USSR used number over number instead of letter over number during its dissolution. The reason for using number over number can be due to difficulty those days of putting fonts into numerator to print for example  Ⴀ , so such emission was just a monument to limits of human progress. 

This  fraction type creates questions: why it was introduced, was it or is it  more practical than the regular style, why there was switch during emission from fraction to regular style in some territories. 

Great research done👏

I am not interested in banknote, however I enjoyed this article. Thanks for sharing! 

In modern world there is one more type of numeration.

Source: https://t.me/s/enjoyyourcollection?q=Libya )
This banknote of 20 dinars is legal tender on the whole territory of Libya (the Numista Team proposes another vision of course, and I strongly disagree with it).
 

It demonstrates structure: numeral(s) - fraction - number. Atop of fraction a letter of local alphabet is situated. The alphabet does not have  upper and lower cases for script, thus just a letter.

This type of fraction in numeration structure of banknotes was and still going in Egyptian Banknotes to this day. one example is The one Egyptian pound.

The Numerator (Letter): Represents the specific note design, minor changes in the design like security feature or lettering on the banknote, does not require change in letter.

Denominator (Number): Indicates the print run or issuance sequence of this particular design( i.e. Series).

Serial Numbering (SN#): Each series includes serial numbers ranging from 1 up to a specified number, usually 6 or 7 digits. 

Even the new modern polymer Egyptian banknotes released in the last two years 10 Pounds (2022-2023) & 20 Pounds (2023) follow the same structure. 

Could there be a typo in the description of a fraction? As far as I see the letter is at its bottom, which in English should be named "denominator."

I understand your concern, but this is because Arabic is read from right to left, and the fraction is written in a single line. So the letter would be first indicating a numerator not denominator.  This can be clearly seen in older designs when fraction was written in two lines. 

For example  10 Pounds ND (1952-1960)

Even before that, during the Egyptian kingdom when numerals were written in English language, 10 Pounds 1931-1951

As seen here the letter in Egyptian banknotes is always numerator not denominator.