Comparando frações em quatro bases numéricas

󱹮 se lê “cunha”; a cunha é usada como separador de raiz para as bases seis e trinta e seis

󱹯 ou „ são chamados “separador de sézima períodica” (base seis/trinta e seis), “separador de dízima periódica” (base dez), coletivamente de “separador periódico” (qualquer base), e são lidos “e repete”; um separador periódico indica que os algarismos à direita dele se repetem indefinidamente

se a parte periódica do número terminar num zero significativo, se trava esse zero significativo usando reticências ...

 

Todas as frações de dois a doze

SeisTrinta e seisDezDoze
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,↋

 

SeisTrinta e seisDezDoze
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,↋

 

Frações unitárias de dois a trinta e seis

SeisTrinta e seisDezDoze
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

 

Padrões regulares na representação base seis das frações de cem

Na tabela abaixo cada linha individual tem a mesma parte periódica, e cada grupo de linhas destacado tem a mesma parte fixa;

Para cada coluna a parte fixa é 0󱹮13 maior do que a coluna à esquerda, e os últimos 3 dígitos da parte periódica seguem uma ordem decrescente, enquanto os 2 dígitos da parte fixa seguem em ordem crescente;

DezSeisDezSeisDezSeisDezSeis
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