Editing Duodecimal (section)

== Conversion tables to and from decimal ==
To convert numbers between bases, one can use the general conversion algorithm (see the relevant section under [[Base conversion|positional notation]]). Alternatively, one can use digit-conversion tables. The ones provided below can be used to convert any duodecimal number between 0.1 and {{d3}}{{d3}},{{d3}}{{d3}}{{d3}}.{{d3}} to decimal, or any decimal number between 0.1 and 99,999.9 to duodecimal. To use them, the given number must first be decomposed into a sum of numbers with only one significant digit each. For example:

:12,345.6 = 10,000 + 2,000 + 300 + 40 + 5 + 0.6

This decomposition works the same no matter what base the number is expressed in. Just isolate each non-zero digit, padding them with as many zeros as necessary to preserve their respective place values. If the digits in the given number include zeroes (for example, 7,080.9), these are left out in the digit decomposition (7,080.9 = 7,000 + 80 + 0.9). Then, the digit conversion tables can be used to obtain the equivalent value in the target base for each digit. If the given number is in duodecimal and the target base is decimal, we get:

:<small>(duodecimal)</small> 10,000 + 2,000 + 300 + 40 + 5 + 0.6 <br> = <small>(decimal)</small> 20,736 + 3,456 + 432 + 48 + 5 + 0.5

Because the summands are already converted to decimal, the usual decimal arithmetic is used to perform the addition and recompose the number, arriving at the conversion result:

 Duodecimal --->  Decimal
   
   10,000    =   20,736
    2,000    =    3,456 
      300    =      432
       40    =       48
        5    =        5
  +     0.6  =  +     0.5
 -----------------------------
   12,345.6  =   24,677.5

That is, <small>(duodecimal)</small> 12,345.6 equals <small>(decimal)</small> 24,677.5

If the given number is in decimal and the target base is duodecimal, the method is same. Using the digit conversion tables:

<small>(decimal)</small> 10,000 + 2,000 + 300 + 40 + 5 + 0.6 <br> = <small>(duodecimal)</small> 5,954 + 1,1{{d2}}8 + 210 + 34 + 5 + 0.{{overline|7249}}

To sum these partial products and recompose the number, the addition must be done with duodecimal rather than decimal arithmetic:

   Decimal --> Duodecimal
   
   10,000    =   5,954
    2,000    =   1,1{{d2}}8
      300    =     210
       40    =      34
        5    =       5
  +     0.6  =  +    0.{{overline|7249}}
 -------------------------------
   12,345.6  =   7,189.{{overline|7249}}

That is, <small>(decimal)</small> 12,345.6 equals <small>(duodecimal)</small> 7,189.{{overline|7249}}

=== Duodecimal to decimal digit conversion ===
{| class="wikitable"
! Duod.
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
|- style="text-align:right"
| style="background:silver;"| '''10,000'''
| 20,736
| style="background:silver;"| '''1,000'''
| 1,728
| style="background:silver;"| '''100'''
| 144
| style="background:silver;"| '''10'''
| 12
| style="background:silver;"| '''1'''
| 1
| style="background:silver;"| '''0.1'''
| style="text-align:left" | 0.08{{overline|3}}
|- style="text-align:right"
| style="background:silver;"| '''20,000'''
| 41,472
| style="background:silver;"| '''2,000'''
| 3,456
| style="background:silver;"| '''200'''
| 288
| style="background:silver;"| '''20'''
| 24
| style="background:silver;"| '''2'''
| 2
| style="background:silver;"| '''0.2'''
| style="text-align:left" | 0.1{{overline|6}}
|- style="text-align:right"
| style="background:silver;"| '''30,000'''
| 62,208
| style="background:silver;"| '''3,000'''
| 5,184
| style="background:silver;"| '''300'''
| 432
| style="background:silver;"| '''30'''
| 36
| style="background:silver;"| '''3'''
| 3
| style="background:silver;"| '''0.3'''
| style="text-align:left" | 0.25
|- style="text-align:right"
| style="background:silver;"| '''40,000'''
| 82,944
| style="background:silver;"| '''4,000'''
| 6,912
| style="background:silver;"| '''400'''
| 576
| style="background:silver;"| '''40'''
| 48
| style="background:silver;"| '''4'''
| 4
| style="background:silver;"| '''0.4'''
| style="text-align:left" | 0.{{overline|3}}
|- style="text-align:right"
| style="background:silver;"| '''50,000'''
| 103,680
| style="background:silver;"| '''5,000'''
| 8,640
| style="background:silver;"| '''500'''
| 720
| style="background:silver;"| '''50'''
| 60
| style="background:silver;"| '''5'''
| 5
| style="background:silver;"| '''0.5'''
| style="text-align:left" | 0.41{{overline|6}}
|- style="text-align:right"
| style="background:silver;"| '''60,000'''
| 124,416
| style="background:silver;"| '''6,000'''
| 10,368
| style="background:silver;"| '''600'''
| 864
| style="background:silver;"| '''60'''
| 72
| style="background:silver;"| '''6'''
| 6
| style="background:silver;"| '''0.6'''
| style="text-align:left" | 0.5
|- style="text-align:right"
| style="background:silver;"| '''70,000'''
| 145,152
| style="background:silver;"| '''7,000'''
| 12,096
| style="background:silver;"| '''700'''
| 1,008
| style="background:silver;"| '''70'''
| 84
| style="background:silver;"| '''7'''
| 7
| style="background:silver;"| '''0.7'''
| style="text-align:left" | 0.58{{overline|3}}
|- style="text-align:right"
| style="background:silver;"| '''80,000'''
| 165,888
| style="background:silver;"| '''8,000'''
| 13,824
| style="background:silver;"| '''800'''
| 1,152
| style="background:silver;"| '''80'''
| 96
| style="background:silver;"| '''8'''
| 8
| style="background:silver;"| '''0.8'''
| style="text-align:left" | 0.{{overline|6}}
|- style="text-align:right"
| style="background:silver;"| '''90,000'''
| 186,624
| style="background:silver;"| '''9,000'''
| 15,552
| style="background:silver;"| '''900'''
| 1,296
| style="background:silver;"| '''90'''
| 108
| style="background:silver;"| '''9'''
| 9
| style="background:silver;"| '''0.9'''
| style="text-align:left" | 0.75
|- style="text-align:right"
| style="background:silver;"| '''{{nowrap|{{d2}}0,000}}'''
| 207,360
| style="background:silver;"| '''{{d2}},000'''
| 17,280
| style="background:silver;"| '''{{d2}}00'''
| 1,440
| style="background:silver;"| '''{{d2}}0'''
| 120
| style="background:silver;"| '''{{d2}}'''
| 10
| style="background:silver;"| '''0.{{d2}}'''
| style="text-align:left" | 0.8{{overline|3}}
|- style="text-align:right"
| style="background:silver;"| '''{{d3}}0,000'''
| 228,096
| style="background:silver;"| '''{{d3}},000'''
| 19,008
| style="background:silver;"| '''{{d3}}00'''
| 1,584
| style="background:silver;"| '''{{d3}}0'''
| 132
| style="background:silver;"| '''{{d3}}'''
| 11
| style="background:silver;"| '''0.{{d3}}'''
| style="text-align:left" | 0.91{{overline|6}}
|}

=== Decimal to duodecimal digit conversion ===
{| class="wikitable"
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
! Duod.
! Dec.
! Duodecimal
|-
| style="background:silver;"| '''10,000'''
| 5,954
| style="background:silver;"| '''1,000'''
| 6{{d3}}4
| style="background:silver;"| '''100'''
| 84
| style="background:silver;"| '''10'''
| {{d2}}
| style="background:silver;"| '''1'''
| 1
| style="background:silver;"| '''0.1'''
| 0.1{{overline|2497}}
|-
| style="background:silver;"| '''20,000'''
| {{d3}},6{{d2}}8
| style="background:silver;"| '''2,000'''
| 1,1{{d2}}8
| style="background:silver;"| '''200'''
| 148
| style="background:silver;"| '''20'''
| 18
| style="background:silver;"| '''2'''
| 2
| style="background:silver;"| '''0.2'''
| 0.{{overline|2497}}
|-
| style="background:silver;"| '''30,000'''
| 15,440
| style="background:silver;"| '''3,000'''
| 1,8{{d2}}0
| style="background:silver;"| '''300'''
| 210
| style="background:silver;"| '''30'''
| 26
| style="background:silver;"| '''3'''
| 3
| style="background:silver;"| '''0.3'''
| 0.3{{overline|7249}}
|-
| style="background:silver;"| '''40,000'''
| 1{{d3}},194
| style="background:silver;"| '''4,000'''
| 2,394
| style="background:silver;"| '''400'''
| 294
| style="background:silver;"| '''40'''
| 34
| style="background:silver;"| '''4'''
| 4
| style="background:silver;"| '''0.4'''
| 0.{{overline|4972}}
|-
| style="background:silver;"| '''50,000'''
| 24,{{d3}}28
| style="background:silver;"| '''5,000'''
| 2,{{d2}}88
| style="background:silver;"| '''500'''
| 358
| style="background:silver;"| '''50'''
| 42
| style="background:silver;"| '''5'''
| 5
| style="background:silver;"| '''0.5'''
| 0.6
|-
| style="background:silver;"| '''60,000'''
| 2{{d2}},880
| style="background:silver;"| '''6,000'''
| 3,580
| style="background:silver;"| '''600'''
| 420
| style="background:silver;"| '''60'''
| 50
| style="background:silver;"| '''6'''
| 6
| style="background:silver;"| '''0.6'''
| 0.{{overline|7249}}
|-
| style="background:silver;"| '''70,000'''
| 34,614
| style="background:silver;"| '''7,000'''
| 4,074
| style="background:silver;"| '''700'''
| 4{{d2}}4
| style="background:silver;"| '''70'''
| 5{{d2}}
| style="background:silver;"| '''7'''
| 7
| style="background:silver;"| '''0.7'''
| 0.8{{overline|4972}}
|-
| style="background:silver;"| '''80,000'''
| 3{{d2}},368
| style="background:silver;"| '''8,000'''
| 4,768
| style="background:silver;"| '''800'''
| 568
| style="background:silver;"| '''80'''
| 68
| style="background:silver;"| '''8'''
| 8
| style="background:silver;"| '''0.8'''
| 0.{{overline|9724}}
|-
| style="background:silver;"| '''90,000'''
| 44,100
| style="background:silver;"| '''9,000'''
| 5,260
| style="background:silver;"| '''900'''
| 630
| style="background:silver;"| '''90'''
| 76
| style="background:silver;"| '''9'''
| 9
| style="background:silver;"| '''0.9'''
| 0.{{d2}}{{overline|9724}}
|}