Simplification of the numbering system

Counting numbers
Numbers are essential for accurate communication and constitute an important element of any language. No language can be complete without words for numbers. Easiness in counting is indicative of simplicity of the language.
The system of counting numbers up to 10 could be related to 10 fingers of both hands. That suggests the rationale behind universal usage of base 10 system also known as decimal system. The concept of zero (0) and increased powers of digits on the left side are directly related to decimal system and positional notation. It is well known that these concepts originated in India.
While the digital notation of numbers is simple and systematic, their text representation in different languages is not always so simple. Although only 10 symbols are used for writing any number in digits (0, 1 to 9), there are numerous words to express them in text form in different languages. For example, in Hindi and most other languages of India, every number up to 100 has a single and unique word. One has to learn 100 words to count up to 100. Knowing every number from 1 to 98 would still not be enough to tell the word for 99. Chinese language, on the other hand, is systematic and has distinct words for the numbers from 1 to 10, and combinations of these 10 words are used all the way up to 100(Burling: 52).
In the English language, although compound words are used to express most numbers of more than one digit, there are complications due to use of single words for numbers of more than one digit from 10 to 19 and differently spelled words for 20, 30, 40 and 50. The positional factor of digital system suggests that the digits and the powers in numbers should be indicated explicitly for accurate counting.
There is no problem in counting single digit numbers in any language since they are expressed in single words which can be written and remembered correctly and accurately. More than one digit numbers, however, imply presence of powers of 10, 100, 1000 or more. In text forms of most languages, higher positional powers of 100, 1000 and more are expressed distinctly but lower power of 10 is not given proper recognition and implied in the word for the digit with which it is associated producing numerous words in different languages.The recognition of the positional power of 10 and its explicit indication in numbering system would simplify counting numbers in any language.

Counting in English
We look at the English language first in which the distortion is minimal and correction would be the simpler. There are three irregularities in English language which may be described as follows:
1 The power of 10 is distinctly recognized in all numbers from 20 to 99 through suffix of ty (as in six ty, nine ty etc.), but not given the status of a separate word along lines of other powers such as hundred, thousand, million etc. WE always say nine hundred (900), five thousand (5000) and eight million (8000000).
2 Four digits, namely, two, three, four and five get distorted when they are associated with the positional power of 10. Thus two becomes twen( ty), three becomes thir( ty), four becomes for( ty) and five becomes fif( ty). Interestingly, there is no change in six, seven, eight and nine.
3 The numbers from 10 to 19 are represented by single words although they incorporate the positional power of 10. They do not follow the logic of the ty suffix which is started from 20.

Correction of these distortions is easy. "ty" could be treated a separate word. "twen", "thir", "for" and "fif" could be replaced by "two", "three", "four" and "five" respectively. Logic of numbering from 20 to 99 could be applied to numbers from 10 to 19 also. Thus, counting of numbers after nine would follow the system of identification of digits and powers distinctly. This way, one has to use only 10 words(9 digits and ty) to count up to 99. Moreover, numbers of up to 15 digits can be counted by using only 15 words! Additional 5 words would be: hundred, thousand, million, billion, and trillion. Thus 10 could be expressed as "one ty" followed by "one ty one", "one ty two", "one ty three" etc. up to "one ty nine". Twenty, thirty, forty and fifty would become two ty, three ty, four ty, and five ty for considerations of uniformity. Six ty, seven ty eigh ty and nine ty will remain as they are. Writing "ty" or "tii" or "ti" as separate word is required in view of its representation of the power of 10 which is similar to "hundred" and "thousand" used as separate words to indicate the power of 100 and 1000 respectively. The number 123456789012345 will be read as "one hundred two ty three trillion four hundred five ty six billion seven hundred eight ty nine million one ty two thousand three hundred four ty five".
For other languages also, the same logic could be applied for text representation of numbers. Single digits would have one word but numbers with more than one digit should be expressed in combination of words representing digits and positional powers.

Counting in Romanaagarii
For languages of India, this suggestion should not be considered too awkward or strange. Sanskrit language uses compound words for numbers with more than one digit. It also incorporates the concept of suffix "tii" to some extent. Shash(6) becomes shashti (60), sapta(7) becomes saptati(70), asht'a(8) becomes asht'i(80) and nava(9) becomes navati (Ballantyne: 10, 14,16). In the most ancient and sacred scripture of India, Rig Veda (1.53.9), there is reference to “Shasti Sahastra Navati Nava” (60099). This is not only the proof of advanced counting system of high numbers known in the Vedic era, but also an indication of a very simple and systematic expression of positional power of digits for counting up to 99 (Navati Nava). Both Shasti and Navati use "ti" as suffix to convey the positional power and imply that 6 and 9 have the values of 60 and 90 respectively. The expression 'navati nava' also implies that counting after each segment of 10 is done through repetition of numbers from 1 to 9 in the same way as it is done in English language counting from 20 onwards. The English language counting is, interestingly, close to the notation of positional power found in the Rig Veda!
It is not clear why the Indian languages did not follow the logic and simplicity of decimal system originated in India long before its use in the western world. "Hindu mathematicians invented zero more than 2,000 years ago. Their discovery led them to positional numbers, simpler arithmetic calculations, negative numbers, algebra with a symbolic notation, as well as the notions of infinitesimals, infinity, fractions, and irrational numbers" (Logan: 152). If the Indian mind could produce such abstract and rational concepts of mathematics, there should be no hesitation in simplifying and rationalizing the numbering system through Romanaagarii not only for Hindi but for other languages also.
While simplifying the numbering system for Hindi, the existing words for digits up to 9, a separate word for positional power of 10(tii), and existing words for powers of 100(soo), 1000(hazaar) may be used. Hindi usage of powers of laakh, karorx etc. is, however, computationally problematic because their progression is based on sequence of groups of two digits which is different from three digit positional power of 1000 which comes before them on the right side. Dividing all the number into groups of three digits would be more logical and systematic. For example, 123456789 would require separate indication of first six digits in groups of two (12 karorx, 34 laakh, 56 hazaar) and then last three digits will be counted as one group. A computer program in this situation will be too complicated. Equal division in groups of three (123 million, 456 hazaar etc.) is simple and systematic. It is, therefore, suggested that million, billion and trillion should be used for higher powered numbers.
The systematic and logical method of writing (and speaking) numbers in text form as suggested here for Romanaagarii will simplify the learning of numbers. Learning 15 words for counting numbers up to trillions may be compared to the existing system of counting in Hindi by learning one hundred words to count up to one hundred only. The table in Appendix 5 incorporates the existing Hindi and suggested Romanaagarii and English versions of text representation of numbers from 0 to 100.
This suggestion may appear to be new but it is not unprecedented. It may be mentioned that modern Welsh has abandoned the vigesimal (reckoning by twenties) system and adopted a wholly decimal system on lines exactly as indicated above (Hurford: 84). It uses the existing words for 1 10 and repeats them after indicating the power of 10. It looks as follows:

Apart from easy method of counting numbers, other justification for accepting the simplified numbering system is its computer compatibility. No program based on the existing text representation of numbers in Hindi can properly transform digits into text or vice versa. By adopting Romanaagarii's numbering system, this task will be made very easy.
Before giving an algorithm or program for this purpose, we should clarify some conventions to be followed in counting numbers and their text and digit representation. We should also mark distinction between small powers (10 and 100) and big powers (1,000, 1,000,000, 1,000,000,000 and beyond).Correct indication of powers and uniformity in expression is essential for accuraate manipulation of any number system. The following rules and conventions are to be followed in this simplified numbering system .

Conventions regarding numbers and digits:
a. There are only 10 digits and a digit is represented by one word, namely, zero, one, two, three, etc. up to nine.
b. In a number of more then one digit, power of the digit is always implied and expressed. 11 is expressed as “one ti one”.
c. First digit of a number cannot be zero(0).
d. In numbers of 3 digits, only small powers of ti (10) and hundred (100) are recognized. 999 is read as “nine hundred nine ti nine”.
e. Numbers of more than 3 digits are to be divided into groups of 3 starting from the right hand side. Groups are to be counted from left side. 1234567890 will have four groups: first group of 1, second group of 234, third group of 567, and fourth group of 890.
f. Leftmost group (first group) may have one, two or three digits. In 123456789 the first group will have 123. In 23456789, the first group will have 23 and in 3456789, the first group will have 3.
g. Digits are read in group from left to right and converted into text accordingly.
h. Zero (0) is counted for grouping but not converted into text.
i. No conjuction is to be used in text. It will not be correct to say “nine hundred and nine ty nine”. It should be “nine hundred nine ty nine”.
j. Powers are mentioned only after non-zero digit. In 203 (two hundred three), no power of 0 is indicated.
k. Power of 100 is expressed after first non-zero digit of 3 digit group.
l. Power of 10 is expressed after second non-zero digit of 3 digit group or first digit of 2 digit number or group (group one only)
m. Small powers may come in any group of the number. In first group, however, if there are three digits, both powers of hundred (100) and ty(10) will be present while in group of two digits, only the power of ty(10) will be present and in group of one digit, no power will be present.
n. Big powers come only when there are more than 3 digits. In a number up to 999, there are only hundreds but in 1000, there is the power of thousand.
o. Big power after group one (in more than 3 digit number) is always implied and expressed.
p. Power after first group is expressed if there is a non-zero digit in the group. In number 1,000,000,000, we say one billion and do not refer to any other power because all digits are zeros.
q. Big powers come sequentially starting from the biggest power. In a number of 13, 14 or 15 digits, the first power will be trillion, then billion, then million and then thousand.
r. A big power cannot be repeated in a number. In number 1,000,000,000,000 we should not say one million million but we should say one trillion.
s. Big power of a group is expressed immediately after last digit (non-zero) of the group or small power of previous non-zero digit in the group but not after a big power. We can say so many hundred million or so many ty thousand but we should not say so many thousand billion or so many million thousand.

Number processing programs
Following the above mentioned conventions, we may develop a program for converting text into digit. The algorithm for such a program will be as follows:
initialize number to 0.
identify word and convert into digit or power. First word will always be a non zero digit.
if the word is for digit, add it to number.
if the word is for power, multiply it to number.
follow conventions for correct transformation and indicate errors, if any.
exit after reading the last word.
print digit version of text.

The algorithm for converting number from digit to text form will be as follows:
count total number of digits and divide them into groups of 3.
convert group one (left side) into text.
identify power after group one and indicate it in the text.
identify digits of subsequent groups and transform them into text.
indicate big powers after each group as appropriate according to conventions.
exit after last digit of last group is identified.
print text version of number.
Based on these algorithms and conventions, it would be easy to make a computer program to convert numbers from digit form to text form and vice versa, in any language written in Romanaagarii. In fact the proposed numbering system is language and script independent. By using the Romanized version of proposed notations of 16 words, the computer program for converting text into digits and vice versa would be made equally valid for all languages. On the other hand, any program on basis of existing textual notation of numbers in Hindi would be too complicated and long.

Romanaagarii method of counting numbers in Hindi/Urdu from ziiro to biliions:

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