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 = 106. 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 101x6, billion is 102x6, trillion is 103x6, and so on. According to the confused American use however, billion is 101∙6+1∙3 and trillion is 101∙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 word-combinations 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 "seven-point-two-five times ten-raised-to-the-ninth-power" 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 kilo-lightyear (resp. 30 kilo-parsec). As one light-year 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 po-ne-indicator (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 p-n-indicator 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 light-speed 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!

Continuation (further explanations, extensions and examples)


No rights reserved Wolfgang G. Gasser 2016-08-31