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