Liczby wymierne.

a) 1,(41)
b) 0,2(1)
c) 27,0(51)


Odpowiedź :

a)

x = 1,(41)

100x = 141,(41)

100x-x = 141,(41)-1,(41)

99x = 140 |:99

x = 140/99 = 1 41/99


b)

x= 0,2(1) 

100x = 21,(1)

10x = 2,(1)

100x-10x = 21,(1)-2,(1)

90x = 19 |:90

x = 19/90


c)

x = 27,0(51)

1000x = 27051,(51)

10x = 270,(51)

1000x-10x = 27051,(51)-270,(51)

990x = 26781 |:990

x = 26781/990 = 27 51/990 = 27 17/330