Comparing fractions in four number bases

󱹮 is read “wedge,” and it’s used as the radix separator for bases six and thirty‐six

󱹯 or ‥ are called “recurring separators,” and are read “and repeats;” a recurring separator indicates that the digits to the right of it repeat indefinitely.

if the recurring part ends in a significant zero, we lock that significant zero with an ellipsis ...

 

All fractions of two to twelve

SixThirty‐sixTenTwelve
1/20󱹮31/20󱹮0̊1/20.51/20.6
1/30󱹮21/30󱹮0̈1/30‥31/30.4
2/30󱹮42/30󱹮0̄2/30‥62/30.8
1/40󱹮131/40󱹮3̇1/40.251/40.3
3/40󱹮433/40󱹮3̄3/40.753/40.9
1/50󱹯11/50󱹯1̇1/50.21/50‥2497
2/50󱹯22/50󱹯2̈2/50.42/50‥4972
3/50󱹯33/50󱹯3̊3/50.63/50‥7249
4/50󱹯44/50󱹯4̄4/50.84/50‥9724
1/100󱹮11/0̇0󱹮0̇1/60.1‥61/60.2
5/100󱹮55/0̇0󱹮0̆5/60.8‥65/60.↊
1/110󱹯051/1̇0󱹯51/70‥142 8571/70‥186 ↊35
2/110󱹯142/1̇0󱹯4̇2/70‥285 7142/70‥351 86↊
3/110󱹯233/1̇0󱹯3̈3/70‥428 5713/70‥518 6↊3
4/110󱹯324/1̇0󱹯2̊4/70‥571 4284/70‥6↊3 518
5/110󱹯415/1̇0󱹯1̄5/70‥571 4285/70‥86↊ 351
10/110󱹯50...0̇/1̇0󱹯0̆6/70‥857 1426/70‥↊35 186
1/120󱹮0431/2̇0󱹮40̊1/80.1251/80.16
3/120󱹮2133/2̇0󱹮1̈0̊3/80.3753/80.46
5/120󱹮3435/2̇0󱹮4̊0̊5/80.6255/80.76
11/120󱹮5131̇/2̇0󱹮1̆0̊7/80.8757/80.↊6
1/130󱹮041/3̇0󱹮41/90‥11/90.14
2/130󱹮122/3̇0󱹮2̇2/90‥22/90.28
4/130󱹮244/3̇0󱹮4̈4/90‥44/90.54
5/130󱹮325/3̇0󱹮2̊5/90‥55/90.68
11/130󱹮441̇/3̇0󱹮4̄7/90‥77/90.94
12/130󱹮522̇/3̇0󱹮2̆8/90‥88/90.↊8
1/140󱹮0󱹯31/4̇0󱹮3󱹯3̊1/100.11/↊0.1‥2497
3/140󱹮1󱹯43/4̇0󱹮4̇󱹯4̄3/100.33/↊0.3‥7249
11/140󱹮4󱹯11̇/4̇0󱹮1̄󱹯1̇7/100.77/↊0.8‥4972
13/140󱹮5󱹯23̇/4̇0󱹮2̆󱹯2̈9/100.99/↊0.↊‥9724
1/150󱹯031󱹭345󱹬242󱹭11/5̇0󱹯33̇5̄󱹬4̈1̈1/110‥091/↋0‥1
2/150󱹯103󱹭134󱹬524󱹭22/5̇0󱹯0̇1̊4̊󱹬2̆2̄2/110‥182/↋0‥2
3/150󱹯134󱹭524󱹬210󱹭33/5̇0󱹯3̇5̄4̈󱹬1̈33/110‥273/↋0‥3
4/150󱹯210󱹭313󱹬452󱹭44/5̇0󱹯1̈33̇󱹬5̄4̈4/110‥364/↋0‥4
5/150󱹯242󱹭103󱹬134󱹭55/5̇0󱹯4̈1̈3󱹬3̇5̄5/110‥455/↋0‥5
10/150󱹯313󱹭452󱹬421󱹭0...0̇/5̇0󱹯1̊4̊2̆󱹬2̄0̇6/110‥546/↋0‥6
11/150󱹯345󱹭242󱹬103󱹭11̇/5̇0󱹯4̊2̆2̄󱹬0̇1̊7/110‥637/↋0‥7
12/150󱹯421󱹭031󱹬345󱹭22̇/5̇0󱹯2̄0̇1̊󱹬4̊2̆8/110‥728/↋0‥8
13/150󱹯452󱹭421󱹬031󱹭33̇/5̇0󱹯5̄4̈1̈󱹬33̇9/110‥819/↋0‥9
14/150󱹯524󱹭210󱹬313󱹭44̇/5̇0󱹯2̆2̄0̇󱹬1̊4̊10/110‥90...↊/↋0‥↊
1/200󱹮031/0̈0󱹮31/120.08‥31/100.1
5/200󱹮235/0̈0󱹮3̈5/120.41‥65/100.5
11/200󱹮331̇/0̈0󱹮3̊7/120.58‥37/100.7
15/200󱹮535̇/0̈0󱹮3̆11/120.91‥6↋/100.↋

 

SixThirty‐sixTenTwelve
1/200󱹮031/0̈0󱹮31/120.08‥31/100.1
1/150󱹯031󱹭345󱹬242󱹭11/5̇0󱹯33̇5̄󱹬4̈1̈1/110‥091/↋0‥1
1/140󱹮0󱹯31/4̇0󱹮3󱹯3̊1/100.11/↊0.1‥2497
1/130󱹮041/3̇0󱹮41/90‥11/90.14
1/120󱹮0431/2̇0󱹮40̊1/80.1251/80.16
1/110󱹯051/1̇0󱹯51/70‥142 8571/70‥186 ↊35
1/100󱹮11/0̇0󱹮0̇1/60.1‥61/60.2
2/150󱹯103󱹭134󱹬524󱹭22/5̇0󱹯0̇1̊4̊󱹬2̆2̄2/110‥182/↋0‥2
1/50󱹯11/50󱹯1̇1/50.21/50‥2497
2/130󱹮122/3̇0󱹮2̇2/90‥22/90.28
1/40󱹮131/40󱹮3̇1/40.251/40.3
3/150󱹯134󱹭524󱹬210󱹭33/5̇0󱹯3̇5̄4̈󱹬1̈33/110‥273/↋0‥3
2/110󱹯142/1̇0󱹯4̇2/70‥285 7142/70‥351 86↊
3/140󱹮1󱹯43/4̇0󱹮4̇󱹯4̄3/100.33/↊0.3‥7249
1/30󱹮21/30󱹮0̈1/30‥31/30.4
4/150󱹯210󱹭313󱹬452󱹭44/5̇0󱹯1̈33̇󱹬5̄4̈4/110‥364/↋0‥4
3/120󱹮2133/2̇0󱹮1̈0̊3/80.3753/80.46
2/50󱹯22/50󱹯2̈2/50.42/50‥4972
5/200󱹮235/0̈0󱹮3̈5/120.41‥65/100.5
3/110󱹯233/1̇0󱹯3̈3/70‥428 5713/70‥518 6↊3
4/130󱹮244/3̇0󱹮4̈4/90‥44/90.54
5/150󱹯242󱹭103󱹬134󱹭55/5̇0󱹯4̈1̈3󱹬3̇5̄5/110‥455/↋0‥5
1/20󱹮31/20󱹮0̊1/20.51/20.6
10/150󱹯313󱹭452󱹬421󱹭0...0̇/5̇0󱹯1̊4̊2̆󱹬2̄0̇6/110‥546/↋0‥6
5/130󱹮325/3̇0󱹮2̊5/90‥55/90.68
4/110󱹯324/1̇0󱹯2̊4/70‥571 4284/70‥6↊3 518
11/200󱹮331̇/0̈0󱹮3̊7/120.58‥37/100.7
3/50󱹯33/50󱹯3̊3/50.63/50‥7249
5/120󱹮3435/2̇0󱹮4̊0̊5/80.6255/80.76
11/150󱹯345󱹭242󱹬103󱹭11̇/5̇0󱹯4̊2̆2̄󱹬0̇1̊7/110‥637/↋0‥7
2/30󱹮42/30󱹮0̄2/30‥62/30.8
11/140󱹮4󱹯11̇/4̇0󱹮1̄󱹯1̇7/100.77/↊0.8‥4972
5/110󱹯415/1̇0󱹯1̄5/70‥571 4285/70‥86↊ 351
12/150󱹯421󱹭031󱹬345󱹭22̇/5̇0󱹯2̄0̇1̊󱹬4̊2̆8/110‥728/↋0‥8
3/40󱹮433/40󱹮3̄3/40.753/40.9
11/130󱹮441̇/3̇0󱹮4̄7/90‥77/90.94
4/50󱹯44/50󱹯4̄4/50.84/50‥9724
13/150󱹯452󱹭421󱹬031󱹭33̇/5̇0󱹯5̄4̈1̈󱹬33̇9/110‥819/↋0‥9
5/100󱹮55/0̇0󱹮0̆5/60.8‥65/60.↊
10/110󱹯50...0̇/1̇0󱹯0̆6/70‥857 1426/70‥↊35 186
11/120󱹮5131̇/2̇0󱹮1̆0̊7/80.8757/80.↊6
12/130󱹮522̇/3̇0󱹮2̆8/90‥88/90.↊8
13/140󱹮5󱹯23̇/4̇0󱹮2̆󱹯2̈9/100.99/↊0.↊‥9724
14/150󱹯524󱹭210󱹬313󱹭44̇/5̇0󱹯2̆2̄0̇󱹬1̊4̊10/110‥90...↊/↋0‥↊
15/200󱹮535̇/0̈0󱹮3̆11/120.91‥6↋/100.↋

 

Unitary fractions from two to thirty-six

SixThirty‐sixTenTwelve
1/20󱹮31/20󱹮0̊1/20.51/20.6
1/30󱹮21/30󱹮0̈1/30‥31/30.4
1/40󱹮131/40󱹮3̇1/40.251/40.3
1/50󱹯11/50󱹯1̇1/50.21/50‥2497
1/100󱹮11/0̇0󱹮0̇1/60.1‥61/60.2
1/110󱹯051/1̇0󱹯51/70‥142 8571/70‥186 ↊35
1/120󱹮0431/2̇0󱹮40̊1/80.1251/80.16
1/130󱹮041/3̇0󱹮41/90‥11/90.14
1/140󱹮0󱹯31/4̇0󱹮3󱹯3̊1/100.11⁄↊0.1‥2497
1/150󱹯031󱹭345󱹬242󱹭11/5̇0󱹯33̇5̄󱹭4̈1̈1/110‥091⁄↋0‥1
1/200󱹮031/0̈0󱹮31/120.08‥31/100.1
1/210󱹯024󱹭340󱹬531󱹭2151/1̈0󱹯23̄0̄󱹭3̆2̇5̇1/130‥076 9231/110‥0↋
1/220󱹮0󱹯231/2̈0󱹮2󱹯2̊1/140.0‥714 2851/120.0‥↊35 186
1/230󱹮0󱹯21/3̈0󱹮2󱹯2̈1/150.0‥61/130.0‥9724
1/240󱹮02131/4̈0󱹮23̇1/160.06251/140.09
1/250󱹯020󱹭412󱹬245󱹭351󱹬433󱹭11/5̈0󱹯242̇󱹭4̈3̆1̆󱹬3̄1̊1/170‥058 823 529 411 764 71/150‥085 792 14↋ 364 29↊ 7
1/300󱹮021/0̊0󱹮21/180.0‥51/160.08
1/310󱹯015󱹭211󱹬3251/1̊0󱹯12̆1̇󱹭2̊0̆5̇󱹬1̈3̇5̈1/190‥052 631 578 947 368 4211/170‥076 ↋45
1/320󱹮01󱹯41/2̊0󱹮1󱹯4̄1/200.051/180.0‥7249
1/330󱹮0󱹯141/3̊0󱹮1󱹯1̄1/210‥047 6191/190.0‥6↊3 518
1/340󱹮0󱹯134󱹭524󱹬210󱹭31/4̊0󱹮1󱹯4̊2̆2̄󱹭0̇1̊1/220.0‥451⁄1↊0.0‥6
1/350󱹯013󱹭220󱹬304󱹭411/5̊0󱹯12̊0̈󱹭0̊4̄0̇󱹬3̇2̈3󱹭41̄1/230‥043 478 260 869 565 217 391 31⁄1↋0‥063 169 484 21
1/400󱹮0131/0̄0󱹮10̊1/240.041‥61/200.06
1/410󱹯012 351/1̄0󱹯13̈0̆󱹭2̇5̊1/250.041/210‥059 153 43↊ 0↋6 2↊6 878 1↋
1/420󱹮0󱹯121󱹭502󱹬434󱹭0531/2̄0󱹮1󱹯1̈0̆4̈󱹭4̊51̊1/260.0‥384 6151/220.0‥56
1/430󱹮0121/3̄0󱹮10̈1/270‥0371/230.054
1/440󱹮01󱹯141/4̄0󱹮1󱹯4̇1/280.03‥571 4281/240.0‥518 6↊3
1/450󱹯011󱹭240󱹬454󱹭431󱹬511/5̄0󱹯12̇0̄󱹭5̄4̄1̊󱹬1̆1/290‥034 482 758 620 689 655
 172 413 793 1		1/250‥04↋7
1/500󱹮0󱹯11/0̆0󱹮1󱹯1̇1/300.0‥31/260.0‥4972
1/510󱹯010󱹭5451/1̆0󱹯155̄1/310‥032 258 064 516 1291/270‥047 8↊↊ 093 598 166 ↋74
 311 ↋28 623 ↊55
1/520󱹮010󱹭431/2̆0󱹮140̊1/320.031 251/280.046
1/530󱹮0󱹯103󱹭134󱹬524󱹭21/3̆0󱹮1󱹯33̇5̄󱹭4̈1̈1/330‥031/290.0‥4
1/540󱹮0󱹯102󱹭041󱹬224󱹭535󱹬143󱹭31/4̆0󱹮1󱹯242̇󱹭4̈3̆1̆󱹬3̄1̊1/340.0‥294 117 647 058 823 51⁄2↊0.0‥429 ↊70 857 921 4↋3 6
1/550󱹯011/5̆0󱹯11/350.0‥285 7141⁄2↋0‥041 455 9↋3 931
1/1000󱹮011/100󱹮11/360.02‥71/300.04

 

Regular patterns in base six representation of hundreths

On the table below, each individual row has the same recurring part, and each highlighted group of rows has the same fixed part;

For each column, the fixed part is 0󱹮13 greater than the previous column, and the last 3 digits of the recurring part flow in decresent order, and the first 2 in crescent order;

TenSixTenSixTenSixTenSix
0.010󱹮00󱹯20󱹭543   0.260󱹮13󱹯20󱹭543   0.510󱹮30󱹯20󱹭543   0.760󱹮43󱹯20󱹭543   
0.020󱹮00󱹯41󱹭530...0.270󱹮13󱹯41󱹭530...0.520󱹮30󱹯41󱹭530...0.770󱹮43󱹯41󱹭530...
0.030󱹮01󱹯02󱹭514   0.280󱹮14󱹯02󱹭514   0.530󱹮31󱹯02󱹭514   0.780󱹮44󱹯02󱹭514   
0.040󱹮01󱹯23󱹭501   0.290󱹮14󱹯23󱹭501   0.540󱹮31󱹯23󱹭501   0.790󱹮44󱹯23󱹭501   
0.050󱹮01󱹯44󱹭444   0.300󱹮14󱹯44󱹭444   0.550󱹮31󱹯44󱹭444   0.800󱹮44󱹯44󱹭444   
0.060󱹮02󱹯05󱹭432   0.310󱹮15󱹯05󱹭432   0.560󱹮32󱹯05󱹭432   0.810󱹮45󱹯05󱹭432   
0.070󱹮02󱹯30󱹭415   0.320󱹮15󱹯30󱹭415   0.570󱹮32󱹯30󱹭415   0.820󱹮45󱹯30󱹭415   
0.080󱹮02󱹯51󱹭402   0.330󱹮15󱹯51󱹭402   0.580󱹮32󱹯51󱹭402   0.830󱹮45󱹯51󱹭402   
0.090󱹮03󱹯12󱹭350...0.340󱹮20󱹯12󱹭350...0.590󱹮33󱹯12󱹭350...0.840󱹮50󱹯12󱹭350...
0.100󱹮03󱹯33󱹭333   0.350󱹮20󱹯33󱹭333   0.600󱹮33󱹯33󱹭333   0.850󱹮50󱹯33󱹭333   
0.110󱹮03󱹯54󱹭320...0.360󱹮20󱹯54󱹭320...0.610󱹮33󱹯54󱹭320...0.860󱹮50󱹯54󱹭320...
0.120󱹮04󱹯15󱹭304   0.370󱹮21󱹯15󱹭304   0.620󱹮34󱹯15󱹭304   0.870󱹮51󱹯15󱹭304   
0.130󱹮04󱹯40󱹭251   0.380󱹮21󱹯40󱹭251   0.630󱹮34󱹯40󱹭251   0.880󱹮51󱹯40󱹭251   
0.140󱹮05󱹯01󱹭235   0.390󱹮22󱹯01󱹭235   0.640󱹮35󱹯01󱹭235   0.890󱹮52󱹯01󱹭235   
0.150󱹮05󱹯22󱹭222   0.400󱹮22󱹯22󱹭222   0.650󱹮35󱹯22󱹭222   0.900󱹮52󱹯22󱹭222   
0.160󱹮05󱹯43󱹭205   0.410󱹮22󱹯43󱹭205   0.660󱹮35󱹯43󱹭205   0.910󱹮52󱹯43󱹭205   
0.170󱹮10󱹯04󱹭153   0.420󱹮23󱹯04󱹭153   0.670󱹮40󱹯04󱹭153   0.920󱹮53󱹯04󱹭153   
0.180󱹮10󱹯25󱹭140...0.430󱹮23󱹯25󱹭140...0.680󱹮40󱹯25󱹭140...0.930󱹮53󱹯25󱹭140...
0.190󱹮10󱹯50󱹭123   0.440󱹮23󱹯50󱹭123   0.690󱹮40󱹯50󱹭123   0.940󱹮53󱹯50󱹭123   
0.200󱹮11󱹯11󱹭111   0.450󱹮24󱹯11󱹭111   0.700󱹮41󱹯11󱹭111   0.950󱹮54󱹯11󱹭111   
0.210󱹮11󱹯32󱹭054   0.460󱹮24󱹯32󱹭054   0.710󱹮41󱹯32󱹭054   0.960󱹮54󱹯32󱹭054   
0.220󱹮11󱹯53󱹭041   0.470󱹮24󱹯53󱹭041   0.720󱹮41󱹯53󱹭041   0.970󱹮54󱹯53󱹭041   
0.230󱹮12󱹯14󱹭025   0.480󱹮25󱹯14󱹭025   0.730󱹮42󱹯14󱹭025   0.980󱹮55󱹯14󱹭025   
0.240󱹮12󱹯35󱹭012   0.490󱹮25󱹯35󱹭012   0.740󱹮42󱹯35󱹭012   0.990󱹮55󱹯35󱹭012   
0.250󱹮13󱹯00󱹭000   0.500󱹮30󱹯00󱹭000   0.750󱹮43󱹯00󱹭000   1.001󱹮00󱹯00󱹭000