
Yota'mik
Mik (numbers) from 0 to 5 Yota'mik is the name of the nazran numeral system resp. the nazran mathematics. In contrast to the decimal system, it contains only 6 different digits (hexal system) and represents rational numbers as continued fractions. This article deals with these particularities and especially highlights the differences to the human numeral system. AnnotationThe nazran symbols for the numbers are shown topright. However, for the sake of simplicity, they aren't used in this article. Instead, arabic digits with a preceding "n" for the purpose of differentiation, are used. Examples: ( 2501 ) is represented as n2501. Numbers converter
Unfortunately the converter can't be displayed without JavaScript.
The hexal systemIn the decimal system, it's counted from 0 to 9, followed by 0, with 1 being attached ahead  thus 10 is formed. Instead, only 0 to 5 is counted in the hexal system, then again 0 follows and 1 is being attached ahead. So instead of 6 number 10 follows (wherein 1 is a six). From there, it's counted again up to 15, followed by 20, etc. It's helpful not to pronounce these hexal numbers as "ten" and "twenty" but "onezero" and "twozero". Because fewer digits are used, hexadecimal numbers seem to be larger in comparison  for example, the decimal 500 corresponds to a nazran n2152. Examples
Decimal  Nazra'yo 
1  n1 
2  n2 
5  n5 
6  n10 
7  n11 
11  n15 
12  n20 
18  n30 

Decimal  Nazra'yo 
100  n244 
102  n250 
108  n300 
129  n333 
200  n532 
1'000  n4'344 
1'080  n5'000 
1'865  n12'345 

Simple fractionsFractions are always represented in the Nazra'yo as [http] continued fraction, which is best explained by some examples:  The number "a second" is displayed as n0.2 in the Nazra'yo.
 The number "a third" is displayed as n0.3 in the Nazra'yo.
 The number "a quarter" is displayed as n0.4 in the Nazra'yo.
 The number "a sixth" is displayed as n0.10 in the Nazra'yo. [n10 is 6]
In this way, there are no infinite decimal places in the usual decimal fractions, as the following table shows: Examples
Fraction  Decimal  Nazra'yo 
1/2  0,5  n0.2 
1/3  0,333333...  n0.3 
1/4  0,25  n0.4 
1/5  0,2  n0.5 
1/6  0,166666...  n0.10 
1/7  0,142857...  n0.11 

Fraction  Decimal  Nazra'yo 
1/8  0,125  n0.12 
1/9  0,111111...  n0.13 
1/10  0,1  n0.14 
1/11  0,090909...  n0.15 
1/12  0,083333...  n0.20 
1/13  0,076923...  n0.21 

Complex fracturesAt first glance, the simple system can also be quite complicated. For example, there's no integer equivalent in the Nazra'yo for the fraction "three quarters" (that's 0.75). One calculates 1 / 0.75 and receives 1.333 ... and thus a fraction again. The problem is handled as follows: The part before the comma is transferred into the result and the remaining fraction is divided further, until (if) it's solved. In the example ¾, this looks like this:  Output number is ¾, also 0,75
 Remove 0 and memorize (n0  Rest 0,75)
 Calculate 1 / 0,75 results in 1,333...
 Remove 1 and memorize (n0.1  rest 0,333...)
 Caculate 1 / 0.333... results in 3
 Remove 3 and memorize (n0.1.3  no rest)
 Result is n0.1.3
A larger example:  Output number is 3,13
 Remove 3 and memorize (n3  rest 0,13)
 Calculate 1/0,13 results in 7.6923...
 Remove 7 and memorize (n3.11  rest 0,6923...) [n11 is decimal 7]
 Calculate 1/0,6923... results in 1,444...
 Remove 1 and memorize (n3.11.1  rest 0,444...)
 Calculate 1/0,444... results in 2,25
 Remove 2 and memorize (n3.11.1.2  rest 0,25)
 Calculate 1/0,25 results in 4
 Remove 4 and memorize (n3.11.1.2.4  kein Rest)
 Result is n3.11.1.2.4
Examples
Decimal  Nazra'yo 
0,1234  n0.12.13.1.1.1.3.1 
0,69777...  n0.1.2.3.4.5 
2,41666...  n2.2.2.2 
0,444444  n0.2.3.1.332'333.15'300'442.1.2 
0.444...  n0.2.3.1 
Sqr(2)  n1.2.2.2... 
Sqr(3)  n1.1.2.1.2.1.2... 
Φ (Phi, golden number)  n1.1.1.1... 
π (Pi, circle constant)  n3.11.24 (approximation to 7 digits) 

Recalculate fractionsThe recalculation of a continued fraction is simple and linear: One begins with the last floating point number, divides 1 with this number, adds the result to the next floating point number and repeats everything until one has passed all decimal points. Here's a detailed example:  Output number is n5.3.32.2 [n32 is decimal 20]
 Calculate 1/2 results in 0,5
 Add 0,5 to the next number (n32) (20 + 0,5 = 20,5)
 Calculate 1/20,5 results in 0,0487...
 Add 0,0487... to the next number (n3) (3 + 0,0487... = 3,0487...)
 Calculate 1/3,0487... results in 0,328
 Add 0,328 to the last number (n5) (5 + 0,328 = 5,328)
 Result is 5,328
Examples in Nazra'yo
Subtraction 
52=3 
5  2 = 3 
Multiplication 
2*2=4 
2 * 2 = 4 
