Question

Zamień ułamek okresowy na zwykły:
a) 0,0(12)
b)10,88(9)
c)5,(32)
d)500,18(12)

Answer 1

A]
x=0,0121212...........
10x=0,121212.........
100x=1,2121212..............
1000x=12,121212...............
1000x-10x=12
990x=12
x=12/990=2/165
b]
x=10,889999999999
10x=108,89999999999
100x=1088,99999999999
1000x=10889,999999999
1000x-100x=10889-1088
900x=9801
x=9801/900
x=1089/100
c]
x=5,323232
100x=532,323232
100x-x=532-5
99x=527
x=527/99
d]
x=500,18121212
100x=50018,121212
10 000x=5001812,121212
10 000x-100x=5001812-50018
9900x=4 951 794
x=4 951 794 /9900=1 650 598/ 3300=825 299 /1650