Matematyka
OCZKO333
2017-06-23 15:19:59
zad 32 zapisz liczbę w postaci ułamka zwykłego a 0,(8) b 1,(9) c 0,(18) d. 0,(48) e.5,(90) f 5,(900)
Odpowiedź
piotrass
2017-06-23 16:19:43

[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]

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