Question

Answer 1

`0.111...=(1)/(9);\ 0.222...=(2)/(9);\ 0.333...=(3)/(9)=(1)/(3);\\\\0.444...=(4)/(9);\ 0.555...=(5)/(9);\ ...`



`0.3\overline{2}=0.3222...=0.1+0.2222...=0.1+(2)/(9)=(1)/(10)+(2)/(9)=(9)/(90)+(20)/(90)=(29)/(90)`


`0.3\overline{2}=(9)/(20)`

other method


`x=0.32222...\ \ \ |\cdot10\\\\10x=3.222...\ \ \ \ |\cdot10\\\\100x=32.222...\\\\100x-10x=32.222...-3.222...\\\\90x=29\ \ \ \ |:90\\\\x=(29)/(90)`