A simplified and less confusing notation for numbers
With growing complexity of society, economics, technology and science, the positional notation based on ten digits has been stretched beyond its limits. This positional decimal system is only practical due to the introduction of different units for the same measurement quantity (e.g. gram and metric ton), and of auxiliary numbers (e.g. million, mega and milli).
Because of the chaotic use of numbers combined with different measurement units and auxiliary numbers, many of us have no ideas of the orders of magnitude involved. It may be general knowledge that mega corresponds to million = 10^{6}. But how much is pico, tera, trillion?
In case of billion and trillion, we have the additional complication that the completely illogical use of American English has been spreading and confusing more and more the whole world. Logically correct: million is 10^{1x6}, billion is 10^{2x6}, trillion is 10^{3x6}, and so on. According to the confused American use however, billion is 10^{1∙6+1∙3} and trillion is 10^{1∙6+2∙3}.
All such problems can easily be removed by a slightly modified version of the rather clumsy exponential "scientific" notation. Apart from digits from zero to nine and minus, only two morphemes (words) must be added: po (pronounced as in "positive"), ne (pronounced as in "negative"). All numbers and corresponding pronounceable wordcombinations can then be created in a schematic way:
0p 
zero.po 
1 
one 


1p 
one.po 
10 
ten 
deca 

2p 
two.po 
100 
hundred 
hecto 

3p 
three.po 
1000 
thousand 
kilo 

4p 
four.po 
10^4 



5p 
five.po 
10^5 



6p 
six.po 
10^6 
million 
mega 

7p 
seven.po 
10^7 



8p 
eight.po 
10^8 



9p 
nine.po 
10^9 
billion 
giga 
(milliard) 
10p 
one.zero.po 
10^10 



11p 
one.one.po 
10^11 



12p 
one.two.po 
11^12 
trillion 
tera 
(billion) 
The principle is quite easy to understand. E.g. three.po is thousand, and "three.po times six.po = nine.po" corresponds to "thousand times million = billion".
The pronunciation of twelve.po instead of one.two.po for 12p is not problematic.
No reasonable person will confuse nine.po with one.two.po or twelve.po, in the same way as billion (milliard) is regularly confused with trillion (billion).
World population is officially assumed to be around 7.4 billion (seven point four milliard) = 9p74 = nine.po seven four in 2016. The number one billion is expressed as 9p1 = nine.po one. To "sevenpointtwofive times tenraisedtotheninthpower" corresponds "nine.po seven two five" = 9p725.
The Milky Way is assumed to have around 11p25 stars and a diameter of (at least) 100 = 2p1 kilolightyear (resp. 30 kiloparsec). As one lightyear consists of 15p946 m ≈ 16p1 m = one.six.po one meter, we get a Milky Way diameter of around 2p1 ∙ 3p1 ∙ 16p1 = 21p1 meter.
Whereas the digits preceding the poneindicator (and expressing order of magnitude) can be pronounced as one number (e.g. sixteen.po instead of one.six.po), the significant digits following the pnindicator must be pronounced separately. Pronouncing 12p11 as twelve.po eleven could suggest eleven trillion (billion) instead of one whole trillion plus one tenth of a trillion. Therefore the number must be pronounced twelve.po one one or one.two.po one one.
The official value of lightspeed c is 8p2997.9245.8 meter per second. Reasonable approximations are 8p2998 m/s and 8p300 m/s. The value 8p300 m/s can further be abbreviated to 8p3 m/s.
Numbers for values between 0 and 1 are created this way:
00n 
zero.zero.ne 
10^100 



01n 
zero.one.ne 
10^99 



88n 
eight.eight.ne 
10^12 
trillionth 
pico 
(billionth) 
89n 
eight.nine.ne 
10^11 



0n 
zero.ne 
10^10 



1n 
one.ne 
10^9 
billionth 
nano 
(milliardth) 
4n 
four.ne 
10^6 
millionth 
micro 

7n 
seven.ne 
10^3 
thousandth 
milli 
permille 
8n 
eight.ne 
10^2 
hundredth 
centi 
percent 
9n 
nine.ne 
10^1 
tenth 
deci 

0p 
zero.po 
10^0 
one 


The principle of creating negative exponents by regular subtraction from zero is simpler and less confusing than mirroring at zero which leads to two versions of zero: +0 and 0. The regular subtraction principle may seem more complicated at the beginning, but due to its effectiveness it is widely used in computer science.
If we subtract …0001 (one) from …0100 (hundred), we get …0099 (ninety nine). If we subtract …0001 from …0000 (zero), we get …9999 with endless leading nines. Thus, p (po) simply means leading zeroes whereas n (ne) means leading nines.
If e.g. the incidence of a given disease is 3n5 = three.ne five (i.e. 0.000,000,5 = 5 ∙ 10^{7}) per year and person, then among a population of 6p1 (one million) we get on average 3n5 ∙ 6p1 = 9n5 = 0.5 cases per year. Over 10 years this results in 1p1 ∙ 9n5 = 0p5 = 5 cases.
No problems arise from the parallel use of the new notation and the already existing ones. In case of integer numbers from 9999 to +9999 the accustomed positional notation may even be preferable. Yet as soon as "." and "," are involved, only the new notation should be used. In German, 103,985 means 2p1039.85 ≈ 2p104 ≈ 2p1 = 100, whereas in English the same expression 103,985 means 5p1039.85 ≈ 5p104 ≈ 5p1, a difference by factor 3p1 = 1000!