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Universal integers

The « Bi lo bi la bi »

Hexadecimal zillions

The universal fraction names:

Bi le pi la bi pri.







bi hri

1 / 16 1

bi hre

1 / 16 2

bi hra

1 / 16 3

bi hro

1 / 16 4

bi hru

1 / 16 5


bi mri

1 /  1, 048 576 1

bi mre

1 /  1, 048 576 2

bi mra

1 /  1, 048 576 3

bi mro

1 /  1, 048 576 4

bi mru

1 /  1, 048 576 5


Remark :   By hri, hre, hra, hro and hru, in pronunciation  – exceptionally –  atch before ar may grow dumb.

Initial h before r becomes silent.  This for the following motivations :

•  Since divisions per zero are forbidden, the following fractions qri, qre, qra, qro, qru don't exist.

The prononciation of these  – inexisting –  fractions would be rather close to : ri, re, ra, ro, ru.

•  The aim of the present universal numbering is  not to require  acrobatics in pronunciation,

but to procure a modern, easy, worldwide-unified and operating hexadecimal numeration.

•  If the voiceless glottal fricative [ h ] succeeded by a trill [ r ] is perfectly pronounceable,

however,  that suite of phonemes is actually uncommon.  Additionally,  a second risk :

Indistinct speakers or inattentive hearers could confound [ bi hri ] and [ bi ηri ] : 1/ 0xE.

In context, a minor risk, since hri, etc. can't occure anywhere else than after one of the five zillionth.

(cf. Magnitudes, Annotations: Point 4. If not  bre, bra, bro, bru and mri keep regulary the preference.

•  Face of these at least three arguments, allowing or supporting this pronunciation facilitation, the unique reason

to-do-not-so would be the contraint of system, the "Systemzwang", with the argument, if so, the even fraction

sixteen is no longer marked by a voiceless consonantTrifling !   No rules, without at least one exception !

The denominator issue from an even, auxiliary digit is characterized by a voiceless consonant, by the writing.

Thus, the International Bureau unanimously decided :

With the universal hexadecimal fraction names, h, before the fraction-signaling r,  remains  – exceptionally –  unpronounced.

Remark, in modern English similary, one writes write, but rightly, one says rite, like "funeral rite".  –  With UNN, that's different :

One pronounces: bi wri, one fifteenth, in contrary, e.g. five millionth (and) four hundredth (of millionth) is nearly pronounced like

[ zi mri fa ra ].   Nearly ?  –  Yes   Since there stays a " little lenght ", i.e. the preceeding vowel is flimsy stressed [ zi mri fa • ra ].

Not too long, in order to avoid the possible confusion :  bi hri  and  bi yri,  one sixteenth and one thirteenth.  (See Expl. 1.1. below.)

Self-evidence :  The universal number names  hi, he, ha, ho  &  hu, of course, last  [ hi ],  [ he ],  [ ha ], [ ho ]   &  [ hu ] ;  worldwide.



One can distinguish principaly, two different cases for the universal fraction names :

1.  ordinary or real fractions ;   like :   P / V  ( two thirds )   or  VT / ZQ  ( thirty-eight fiftieths ) .

2.  hexadecimal fractions ;   like Q.t   or   BQQ.kqf  i.e. the fractional part of numbers.


1.1.  Plain fractions.   Examples:







pi vri

two thirds





vi fri

three quarters 





vi zri

three fifths





peti kri

twonety-eight twelfths



bi sra

one six hundredth





1.2.  "Unplain" fractions.  Examples:







bi bepri

one onety-seconds 



sedi katre

sixty-seven, twelve hundred eighths



seqi tesri

sixty (units), eighty-sixths 



baqi sefri

one hundred (units), sixty-fourths







1.3.  Composed fraction, integer main denominator.  Example:


si dri kri

six sevenths,

divided by twelve


1.4.  Composed fraction, fraction as main denominator.  Example:


ti kri


pi sri

eight twelfths,

divided by

two sixths




2.    Hexadecimal fractions.  Examples:



qi bri taseti bro

zero units, eight hundred sixty-eight thousands




ba bri ti mri si hri

one hundred units, eight millionth and six sixteenths of millionth




qi bri qi mri fi hra

zero units, zero millionth and eight thousands of millionth



With the hexadecimal fractions, i.e. the fractional part of hexadecimal numbers, there are no difficulties at all.

However, two conventions by the hexadecimal fractions :

1.  The five fraction names which are hexadecimal multiples of one  (bri, bre, bra, bro & bru) are always relative to the unit.

Bi bri  is one oneth (translated by unit),  bi bre : one onetieth,  bi bra : one hundredth,  bi bro : one thousandth and  bi bru  is one onety-thousandth.

In contrary, the five fraction names multiples of sixteen  (hri, hre, hra, hro & hru) are relative to the preceeding zillionth.

Bi hri is one sixteenth (not say : onetieth), bi hre : one hundredth,  bi hra : one thousands,  bi hro : one sixteen-thousandth and bi hru is one millionth,

but always relative to the preceeding zillionth  –   Thus, the hypothetical UNN-numbers  " bi bri si hri or " bi bri qi mre be bra "  don't exist.

2.  The aytch [ h ]   – before the fraction-signaling ar [ r ] or [ R ] –  in  hri, hre, hra, hro & hru  is not pronounced.  (See above.)


Explanation concerning ordinary fractions :

1.1.  Up to one millionth, there are exactly 75 (= 15 Χ 5)  so-called  plain fractions. They all have either an integer denominator

inside the interval one to fifteen, or, if the denominator is greater than fifteen, then the denominator is their basic multiple,

i.e. issue of a multiplication by sixteen to its first, second, third or fourth power. Example :  N  / SQQ is ever a plain fraction.

In other words, in a plain fraction the denominator is either one single digit, or all the following digits are equal zero.

In pronontiation no plain fraction including e.g. bi wra (one fifteen hundredth) or bi xri (one fourteenth) pose any problem

excepting the thirteenths. An isolated « yri » is very difficult to pronounce, without an additional, fugitive, faint vowel :  [ j i r i ].

However in practice, this is not even necessary, since each fraction posseeds a numerator.  Example : BQQ   YQQQQ ,

one hundred thirteenty-thousandths, ba yru  [ ba jru ].  By binding to the preceeding vowel, no-more pronunciation problem.

Similary e.g.  bo yra  or  be yri  pose no difficulties at all. Alone by  bi yri   – y after i –   i is perceptibly lengthened  [ bi : ri ].

1.2.  In so-called unplain fractions, the denominator is expressed in UNN by two or more syllabels. The only difficulty by the

unplain fractions is to distinguish, for example, one hundred sixty-fourth and the plain fraction one hundred sixty quarters.

By unplain fractions, if the ones-digit of the numerator equals zero, one however adds the syllabel -qi, signaling the unit .

Indeed e.g.  BSQ / F, base fri, one hundred sixty quarters is not identical to  BQQ  / SF, ba sefri, one hundred sixty-fourth.

If the appropriated prosody may be able to avoid confusions, to say  baqi sefri  excudes all ambiguities.  That's good style.

This elegant and effective proceeding is also indicated by integers with a following fraction, even with a plain fraction :

Thus,  baqi bi fri,  BQQ B / F is one hundred units and a quarter, in opposite to  babi fri,  BQB / F,  one hundred one quarters.

1.3.  There are no difficulties by composed fractions with an integer main denominator,

1.4.  nor by composed fractions with a fraction as main denominator. Simply, the main fraction is expressed by le, divided by.



This page is online since 2007, March 04