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Rozwiązane

Zamień ułamek okresowy na ułamek zwykły.

0,(31) =
1,(315) =
0,2(31) =
3,0(54) =
0,(9) =

Odpowiedź :

Naomi9640go

A) 0,(31)

x = 0,(31)

100x = 31,(31)

100x - x = 31,(31) - 0,(31)

99x = 31

x = 31/99

B) 1,(315)

x = 1,(315)

1000x = 1315,(315)

1000x - x = 1315,(315) - 1,(315)

999x = 1314

x = 1314/999 = 1 i 315/999 = 1 i 35/111

C) 0,2(31)

10x = 2,(31)

1000x = 231,(31)

1000x - 10x = 231,(31) - 2,(31)

990x = 229

x = 229/990

D) 3,0(54)

10x = 30,(54)

1000x = 3054,(54)

1000x - 10x = 3054,(54) - 30,(54)

990x = 3024

x = 3024/990 = 3 i 54/990 = 3 i 6/110

E) 0,(9)

x = 0,(9)

10x = 9,(9)

10x - x = 9,(9) - 0,(9)

9x = 9

x = 9/9 = 1

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