Question

9. Przedstaw poniższe liczby wymierne w postaci ułamków zwykłych:
a) 0,(225) b) 0,(18) c) 2,(4) d) 5,4(3) e) 1,2(13) f) -0,1(234)

Answer 1

Odpowiedź:

Szczegółowe wyjaśnienie:

0,(225) = x * 1000

0,(225) * 1000 = x * 1000

0,225… * 1000 = 1000x

225,(225) = 1000x  

225,(225) - x = 10x - x

225,(225) - 0,(225) = 10x - x

225 = 999x

999x = 225

x = 225 : 999

x = 225/999

0,(225) = 225/999 = 75/333 = 25/111

0,(18) = x * 100  

0,(18) * 100 = x * 100

18,(18) - x = 100x - x

18,(18) - 0,(18) = 100x - x

18 = 99x

99x = 18

x = 18/99

0,(18) = 18/99 = 6/33 = 2/11

2,(4) = x * 10

2,(4) * 10 = x * 10

24,(4) - x = 10x - x

24,(4) - 2,(4) = 10x - x

22 = 9x

9x = 22

x = 22/9

2,(4) = 22/9 = 2 i 4/9

5,4(3) = 54,(3)  

54,(3) = x * 10

543,(3) -x = 10x - x

543,(3) - 54,(3) = 10x - x

489 = 9x

9x = 489

x = 489/9

5,4(3) = 54,(3) : 10 = 489/9 * 10 = 489/90 = 163/30 = 5 i 13/30

1,2(13) = 12,(13)  

12,(13) = x * 100

1213,(13) - 12(13) = 100x - x

1201 = 99x

99x = 1201

x = 1201/99

1,2(13) = 12,(13) : 100 = 1201/99 * 100 = 1201/990 = 1 i 211/999

-0,1(234) = -1(234)

-1(234) = x * 1000

-1234,(234) - 1(234) = 1000x - x

-1233 = 999x

999x = -1233

x = -1233/999

-0,1(234) = -0,1(234) : 10 = -1233/999 * 10 = -1233/9990 = -411/3330 = -137/1110