Question

Zamień podane ułamek okresowe na ułamki zwykłe.
a)
x 0,(3)
10x=......
-x=0,33333333
9x=......
x=......
x=........

b)
y=0,(15)
100y=.............
-y=0,15151515
y=.......
y=..........
y=.........

c)
x=0,1(5)
100x=............
-10x=...........
90x=..........
x=...........
x=............
x=...........

d)
y=3,1(21)
y=...........
... y=................
-y=............................
.... y=................
y=............
y=..........
y=........

Answer 1

A)
x=0,(3) [/*10]
10x=3,(3)
10x-x=3,(3)-0,(3)
9x=3 [/:9]
x=1/3

b)
y=0,(15) [/*100]
100y=15,(15)
100y-y=15,(15)-0,15
99y=15 [/:99]
y=5/33

c)
x=0,1(5) [/*10]
10x=1,(5) [/*10]
100x=15,(5)
100x-10x=15,(5)-1,(5)
90x=14 [/:90]
x=7/45

d)
y=3,1(21) [/*10]
10y=31,(21) [/*100]
1000y=3121,(21)
1000y-10y=3121,(21)-31,(21)
990y=3090 [/:990]
y=103/33
y=3 i 4/33