Question

exercițiul 7 va rog !!!

Answer 1

a)  0,(3) = 3 / 9 = 1 / 3 
     0,1(6) = ( 16 - 1) / 90 = 15 / 90 = 1 / 6 

1 / 3  × 1 / 6 = 1 / 18

b)  
0,25 = 25 / 100 = 1 / 4 

1 / 4 ×  4 / 5 = 1 / 5 

c) 
0,(13) = 13 / 99 

13 / 99 × 10 / 39 = 10 / 99 × 3 =  10 / 297 

d) 

1,2(9) = ( 129 - 12) / 90 = 117 / 90 = 39 / 30 = 13 / 10 

13 / 10 ×  10 / 3 = 13 / 3 = 4,(3)

Answer 2

a) 0,(3)*0,1(6)=(3/9)*(16-1)/90=(3/9)*(15/90)=(3/9)*(1/6)=3/54=1/18
b)0,25*4/5=1/5,      c)0,(13)*(10/39)=(13/99)*(10/39)=(1/99)*(10/3)=10/297
d)1,2(9)*(10/3)=[(129-12)/90]*(10/3)=(117/90)*(10/3)=(39/9)*(1/1)=39/9=13/3