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Sezimal is a base six number notation and nomenclature; others may refer to sezimal base as sextal, heximal, seximal, senary, or simply base six;
You can see how sezimal works by using the Sezimal Calculator.
Sezimal groups digits in the traditional way of three‐digits grouping, naming each power of six accordingly:
0 zero | 10 six | 20 dozen | 30 thirsy |
1 one | 11 seven | 21 dozen-one | ... ... |
2 two | 12 eight | 22 dozen-two | 40 foursy |
3 three | 13 nine | 23 dozen-three | ... ... |
4 four | 14 ten | 24 dozen-four | 50 fifsy |
5 five | 15 eleven | 25 dozen-five | ... ... |
For 10² we use the numeral nif, from the Ndom word for «thirty-six»; up until here, it’s the same system proposed by jan Misali;
For 10³, we use the numeral arda, from the Sanskrit word अर्ध ‹ardha› /ˈɐɾ.d̪ʱɐ/ for «half» (of six), pronounced roughly as AHR-duh in English; we separate ardas from nifs with the “arda separator”, a narrow non-break space:
100 nif | 1000 arda | 10000 six arda | 100000 nif arda |
200 two nif | 2000 two arda | 20000 dozen arda | 200000 two nif arda |
300 three nif | 3000 three arda | 30000 thirsy arda | 300000 three nif arda |
400 four nif | 4000 four arda | 40000 foursy arda | 400000 four nif arda |
500 five nif | 5000 five arda | 50000 fifsy arda | 500000 five nif arda |
For 10¹⁰, we use the numeral shadara, from the Sanskrit word षडर ‹ṣaḍara› /ʂɐ'ɖɐ.ɾɐ/ for (a wheel that has) «six spokes» (forming a hexagonal shape inside a circle), pronounced like shuh-DAH-ruh; we separate shadaras from nif ardas with a “shadara separator”:
1000000 shadara | 10000000 six sh. | 100000000 nif sh. |
2000000 two sh. | 20000000 dozen sh. | 200000000 two nif sh. |
3000000 three sh. | 30000000 thirsy sh. | 300000000 three nif sh. |
4000000 four sh. | 40000000 foursy sh. | 400000000 four nif sh. |
5000000 five sh. | 50000000 fifsy sh. | 500000000 five nif sh. |
The shadara separator, when followed exclusively by zeroes, may function as an abbreviation for the six zeroes:
1000 arda sh. | 10000 six arda sh. | 100000 nif arda sh. |
2000 two arda sh. | 20000 dozen arda sh. | 200000 two nif arda sh. |
3000 three arda sh. | 30000 thirsy arda sh. | 300000 three nif arda sh. |
4000 four arda sh. | 40000 foursy arda sh. | 400000 four nif arda sh. |
5000 five arda sh. | 50000 five arda sh. | 500000 five nif arda sh. |
The powers 10²⁰, 10³⁰ etc. form their names using Shastadari Prefixes, assuming the “sha” in shadara is a prefix for the sixth power:
10²⁰ | 1000000000000 | dishadara |
10³⁰ | 1000000000000000000 | trishadara |
10⁴⁰ | 1000000000000000000000000 | charshadara |
10⁵⁰ | 1000000000000000000000000000000 | panshadara |
10¹⁰⁰ | 1000000000000000000000000000000000000 | nidara |
10¹¹⁰ | 1000000000000000000000000000000000000000000 | nishadara |
10¹²⁰ | 1000000000000000000000000000000000000000000000000 | nidishadara |
To separate the integer part from the fractional/sezimal part of a number, we use the sezimal separator ― a vertical, thin wedge, point upwards, going up from the lowest position of the font’s descenders, up to the middle of the font’s x‐height, called simply “wedge”:
12345011054321
arda and shadara separators are used both
to the left and the right of the sezimal separator
(one) shadara, two nif thirsy four arda, five nif one wedge one zero five, four three two, one
If you don’t have access to those separators, use the same ones your language/country already uses:
1,234,501.105 432 1
1 234 501.105 432 1
1.234.501,105 432 1
1 234 501,105 432 1
Finally, whenever we find needed or useful to indicate recurring digits on the fraction part of a number, we use the following recurring digit notation:
01 / 0‥1 / 0„1 = 0.111… = 0.1̅ = 1⁄5 (zero and repeats one)
005 / 0‥05 / 0„05 = 0.050505… = 0.0̅5̅ = 1⁄11 (zero and repeats zero five)
003 / 0.0‥3 / 0,0„3 = 0.0333… = 0.03̅ = 1⁄14 (zero wedge zero and repeats three)
000350… / 0.003‥50… / 0,003„50… = 0.0035̅0̅ = 1⁄132 (zero wedge zero zero three and repeats five zero)
So, by writing the fractional separator twice, we indicate that what comes to the right of it repeats indefinitely; if the recurring part ends with at least one significant zero, we lock those significant zeroes at the right with an ellipsis.
With decimal: https://en.wiktionary.org/wiki/decem#Latin
Most descendant languages have changed the /k/ into an /s/ (French writes ‹x› but it’s not pronounced /ks/ or /k/).
The orthographic ‹c› or ‹z› in most languages is pronounced /s/, sometimes /z/ or /tʃ/.
So, /de.kem/ > /de.sem/ > /des/ + imal = decimal /de.si.mal/ (it kept the /s/ pronunciation because it originally was not an /s/, but a /k/, the ‹c› in the orthographies indicates just that).
For six what happens is: https://en.wiktionary.org/wiki/sex#Latin
No language descendant from Latin has kept the /ks/ pronunciation for the number (again, French writes ‹x› but it’s not pronounced /ks/).
They either have open syllables (ending an a vowel or diphthong), or have an /s/ coda; an /s/ intervocalic, in most romance languages, is vocalized into a /z/.
So, /seks/ > /ses/ > /ses/ + imal > /se.zi.mal/ ‹sezimal› (it was originally an /ks/, the /k/ dropped, and the /s/ vocalized to /z/ between vowels).