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General system of units in SMH :    1. Magnitudes  &   2. Ranks

1.  The magnitudes :  There are onety-five ( = 21₁₀ )  magnitudes in SMH.

English hexadecimal number name	1024 N Magnitude equals N.	Ten magnitudes multiple of the base unit :  hexa-i-unit  and ten submultiple-magnitudes.		Hexadecimal number one quintillion – one quintillionth	Universal number name
one quintillion	=  102410	B WiU	one weka -i-unit	B,QQQQQ,QQQQQ,QQQQQ,QQQQQ,QQQQQ	bi mu
four hundred quadrillion	=  1024 9	B XiU	one xona -i-unit	FQQ,QQQQQ,QQQQQ,QQQQQ,QQQQQ	fa mo
one quadrillion	=  1024 8	B YiU	one yotta -i-unit	B,QQQQQ,QQQQQ,QQQQQ,QQQQQ	bi mo
four hundred trillion	=  1024 7	B ZiU	one zetta -i-unit	FQQ,QQQQQ,QQQQQ,QQQQQ	fa ma
one trillion	=  1024 6	B EiU	one  exa -i-unit	B,QQQQQ,QQQQQ,QQQQQ	bi ma
four hundred billion	=  1024 5	B PiU	one peta -i-unit	FQQ,QQQQQ,QQQQQ	fa me
one billion	=  1024 4	B TiU	one tera -i-unit	B,QQQQQ,QQQQQ	bi me
four hundred million	=  1024 3	B GiU	one giga -i-unit	FQQ,QQQQQ	fa mi
one million	=  1024 2	B MiU	one mega -i-unit	B,QQQQQ	bi mi
four hundred	=  1024 1	B kiU	one kilo -i-unit	FQQ	fa
one	=  1024 0	B hiU	one hexa -i-unit	B	bi
four thousandth	=  1024 -1	B miU	one milli -i-unit	Q.qqf	fa bro
one millionth	=  1024 -2	B µiU	one micro -i-unit	Q.qqqqb	bi mri
four thousandth of millionth	=  1024 -3	B niU	one nano -i-unit	Q.qqqqq,qqf	qi mri fa hra*
one billionth	=  1024 -4	B piU	one pico -i-unit	Q.qqqqq,qqqqb	bi mre
four thousandth of billionth	=  1024 -5	B fiU	one femto -i-unit	Q.qqqqq,qqqqq,qqf	qi mre fa hra
one trillionth	=  1024 -6	B aiU	one atto -i-unit	Q.qqqqq,qqqqq,qqqqb	bi mra
four thousandth of trillionth	=  1024 -7	B ziU	one zetta -i-unit	Q.qqqqq,qqqqq,qqqqq,qqf	qi mra fa hra
one quadrillionth	=  1024 -8	B yiU	one yocto -i-unit	Q.qqqqq,qqqqq,qqqqq,qqqqb	bi mro
four thousandth of quadrillionth	=  1024 -9	B xiU	one xonto -i-unit	Q.qqqqq,qqqqq,qqqqq,qqqqq,qqf	qi mro fa hra
one quintillionth	=  1024-10	B wiU	one wecto -i-unit	Q.qqqqq,qqqqq,qqqqq,qqqqq,qqqqb	bi mru

* Remark :  According to an official pronunciation licence, it isn't considered to be false, when by this universal fraction name  the initial H before R grows dumb.

Thus, one always writes :  qi mri fa hra  – i.e. zero millionth, four thousandth (of millionth) –  but one may pronounce :    instead of    .

Annotations:

1. Next to the current, well-known, twice eight magnitudes, with prefixes from yocto -  (= 1000 ^-8)  to yotta -  (= 1000 ⁸)  and the base unit, the hexadecimal

SI recognizes twice two new prefixes :  xona-, weka-  and  xonto-, wecto-, respectively the hexadecimal magnitudes 1024 to power 9, 10 and -9, -10.

For further information concerning these four new prefixes, please see here.

2. The English zillion names are – of course – in analogy to the good old British long scale. Indeed, since Nicolas Chuquet 1484, the only consistent way

is, that the prefix of the -illion is exactly the logarithm of million. So, the decimal trillion equals 1, 000 000 ³, just like the hexadecimal trillion is 1, 048 576 ³.

3. The weka-i-unit is the largest magnitude, i.e. one hexadecimal quintillion (= 1, 048 576 ⁵). The highest value that can be expressed with the universal

number names is exactly 1, 048 576 times greater : Sixteen weka-u-units equals hu mu units.  Thus :  H WuU = HQQQQ × M ^Z, the largest numeral.

(Some quibbling noses may be tented to continue after : hu mu, i.e. a million quintillion, by counting now : hu mu bi, hu mu pi, etc. till maximal two million quintillion minus one. But really, this is not admitted.)

All numbers above a million quintillion, they occur very seldom in serious calculations, can't be expressed in UNN, only by exponentiation expressions.

Similarly, the smallest universal number  – except exponentiation expressions –  is a millionth of quintillionth :  qi mru bi hru,  i.e. in fact  one sextillionth.

4. Bri, bre, bra, bro and bru means respectively oneth, onetieth, hundredth, thousandth and onety-thousandth,  but always relative to the unit.

Hri, hre, hra, hro and hru means respectively sixteenth, hundredth, thousandth, sixteen-thousandth and millionth, relative to the last zillionth.

5. The symbols of unit are always read, just like in decimal SI, in their full meaning. Example :  « him » is to read as hexa-i-metre, never like a word :  him.

All multiples and submultiples of all units of SMH may be read in all languages according to the uses of the languages. This is not the case with UNN.

Languages, like the French-one, not pronouncing H letters, can pronounce hexa-units like exa-units (same etymology). Therefore, orally, the exa-unit becomes the sexa-unit, by keeping the symbol E.

2.  The ranks :  There are always five ranks inside each magnitude.

It's convenient to distinguish the odd magnitudes (like e.g. 1024 ¹, with the prefix kilo)

and the even magnitudes (like for example 1024 ², with the prefix mega, also in SMH).

2.1. The even magnitudes  – here in the table, only from the tera-i-unit to the pica-i-unit –  and their respective five ranks.

Even magnitudes	SHOL Number	Universal number name	English hexadecimal number name	Decimal value
B TiU one tera -i-unit	B,QQQQQ,QQQQQ	bi me	one billion	1, 099 511, 627 776
B MuU one mega -u-unit B MoU one mega -o-unit B MaU one mega -a-unit B MeU one mega -e-unit B MiU one mega -i-unit	BQQQQ,QQQQQ BQQQ,QQQQQ BQQ,QQQQQ BQ,QQQQQ B,QQQQQ	bu mi bo mi ba mi be mi bi mi	onety thousand million one thousand million one hundred million onety million one million	68 719, 476 736   4 294, 967 296   268, 435 456   16, 777 216   1, 048 576
B huU one hexa -u-unit B hoU one hexa -o-unit B haU one hexa -a-unit B heU one hexa -e-unit B hiU one hexa -i-unit	BQQQQ BQQQ BQQ BQ B	bu bo ba be bi	onety thousand one thousand one hundred onety one	65 536   4 096   256   16   1
B µuU one micro -u-unit B µoU one micro -o-unit B µaU one micro -a-unit B µeU one micro -e-unit B µiU one micro -i-unit	Q.b Q.qb Q.qqb Q.qqqb Q.qqqqb	qi bri bi bre qi bri bi bra qi bri bi bro qi bri bi bru qi bri bi mri	one onetieth one hundredth one thousandth one onety-thousandth one millionth	16  -1 256  -1 4 096  -1 65 536  -1 1, 048 576  -1
B puU one pico -u-unit B poU one pico -o-unit B paU one pico -a-unit B peU one pico -e-unit B piU one pico -i-unit	Q.qqqqq,b Q.qqqqq,qb Q.qqqqq,qqb Q.qqqqq,qqqb Q.qqqqq,qqqqb	qi mri bi hri qi mri bi hre qi mri bi hra qi mri bi hro qi mri bi hru	one sixteenths of a millionth one hundredth of a millionth one thousandth of a millionth one sixteen-thousandth of a millionth one billionth	16, 777 216  -1 268, 435 456  -1 4 294, 967 296  -1 68 719, 476 736  -1 1, 099 511, 627 776  -1

Next to this main system of even magnitudes  – clearly predominant in the applied sciences –  there exists a so-called secondary system of odd magnitudes.

The odd magnitudes remain present with its length units like foot (milli-a-metre), digit (milli-a-metre) or in the mass units : talent (kilo-e-gram),  franc (milli-u-gram).

2.1. The odd magnitudes  – here in the table, only from the giga-o-unit to the femto-a-unit –  and their respective ranks.

Odd magnitudes	SHOL Number	Universal number name	English hexadecimal number name	Decimal value
B GoU one giga -o-unit	F,QQQQQ,QQQQQ	fi me	four billion	4, 398 046, 511 104
B GaU one giga -a-unit B GeU one giga -e-unit B GiU one giga -i-unit B kuU one kilo -u-unit B koU one kilo -o-unit	FQQQQ,QQQQQ FQQQ,QQQQQ FQQ,QQQQQ FQ,QQQQQ F,QQQQQ	fu mi fo mi fa mi fe mi fi mi	forty thousand million four thousand million four hundred million forty million four million	274 877, 906 944   17 179, 869 184   1 073, 741 824   67, 108 864   4, 194 304
B kaU one kilo -a-unit B keU one kilo -e-unit B kiU one kilo -i-unit B muU one milli -u-unit B moU one milli -o-unit	FQQQQ FQQQ FQQ FQ F	fu fo fa fe fi	forty thousand four thousand four hundred forty four	262 144   16 384   1 024   64   4
B maU one milli -a-unit B meU one milli -e-unit B miU one milli -i-unit B nuU one nano -u-unit B noU one nano -o-unit	Q.f Q.qf Q.qqf Q.qqqf Q.qqqqf	qi bri fi bre qi bri fi bra qi bri fi bro qi bri fi bru qi bri fi mri	four onetieths four hundredths four thousandths four onety-thousandths four millionth	4  -1 64  -1 1 024  -1 16 384  -1 262 144  -1
B naU one nano -a-unit B neU one nano -e-unit B niU one nano -i-unit B fuU one femto -u-unit B foU one femto -o-unit	Q.qqqqq,f Q.qqqqq,qf Q.qqqqq,qqf Q.qqqqq,qqqf Q.qqqqq,qqqqf	qi mri fi hri qi mri fi hre qi mri fi hra qi mri fi hro qi mri fi hru	four sixteenths of a millionth four hundredths of a millionth four thousandths of a millionth four sixteen-thousandths of a millionth four billionth	4, 194 304  -1 67, 108 864  -1 1 073, 741 824  -1 17 179, 869 184  -1 274 877, 906 944  -1
B faU one femto -a-unit	Q.qqqqq,qqqqq,f	qi mre fi hri	four sixteenths of a billionth	4, 398046, 511 104  -1

The fact that  – for example –  the 4^th rank of magnitude -1 is four basic units can be neglected, till one stays inside the odd, the secondary system.

Example :  B milli-o-metre (i.e. one perch)    equals    BQ milli-a-metres (i.e. onety feet)    equal    BQQ milli-e-metres (i.e. one hundred digits).

Only at the moment when one desires to convert to the main system of even magnitudes, one have to remember the conversion factor 1024  =  FQQ.

B milli-o-metre (one perch)   =   FQQ micro-o-metres (four hundred lines)   =   FQ micro-u-metres (forty palms)   =   F hexa-i-metres (four aunes).

Self-evidence :  In all experimental, scientific contexts, the lost of precision caused by those conversions must be indicated.  Example :  B.tv him  =  S.qk mam  (± Q.qp mam).

 

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