[latex]0,(8)=x[/latex] [latex]x=0,8888ldots[/latex] [latex]10x=8,8888ldots[/latex] [latex]10x-x=8,8888ldots-0,8888ldots[/latex] [latex]9x=8[/latex] [latex]x=cfrac{8}{9}[/latex] [latex]0,(8)=cfrac{8}{9}[/latex] [latex]1,(9)=x[/latex] [latex]x=1,9999ldots[/latex] [latex]10x=19,9999ldots[/latex] [latex]10x-x=19,9999ldots-1,9999ldots[/latex] [latex]9x=18[/latex] [latex]x=2[/latex] [latex]1,(9)=2[/latex] [latex]0,(18)=x[/latex] [latex]x=0,18181818ldots[/latex] [latex]100x=18,18181818ldots[/latex] [latex]99x=18[/latex] [latex]x=cfrac{18}{99}[/latex] [latex]0,(18)=cfrac{18}{99}[/latex] [latex]0,(48)=x[/latex] [latex]x=0,48484848ldots[/latex] [latex]100x=48,48484848ldots[/latex] [latex]99x=48[/latex] [latex]x=cfrac{48}{99}[/latex] [latex]0,(48)=cfrac{48}{99}[/latex] [latex]5,(90)=x[/latex] [latex]x=5,909090ldots[/latex] [latex]100x=590,909090ldots[/latex] [latex]99x=585[/latex] [latex]x=cfrac{585}{99}=5cfrac{90}{99}=5cfrac{10}{11}[/latex] [latex]5,(900)=x[/latex] [latex]x=5,900900900ldots[/latex] [latex]1000x=5900,900900900ldots[/latex] [latex]999x=5895[/latex] [latex]x=cfrac{5895}{999}=5cfrac{900}{999}=5cfrac{100}{111}[/latex]