$Đáp$ $án$ $+$ $Giải$ $thích$ $các$ $bước$ $giải$ $:$

`tt\color{#36648B}{\text{ϟҡıṅɢṃåṭһṡ ⚡︎}`

$a)$ `0,(3) = 0,(1) . 3 = 1/9 . 3 = 1/3`

$b)$ `1,(3) = 1 + 0,(3) = 1 + 0,(1) . 3 = 1 + 1/9 . 3 = 1 + 1/3 = 4/3`

$c)$ `4,(5) = 4 + 0,(5) = 4 + 0,(1) . 5 = 4 + 1/9 . 5 = 4 + 5/9 = 41/9`

$d)$ `-0,151515... = -0,(15) = -0,(01) . 15 = {-1}/99 . 15 = {-5}/33`

$e)$ `6,(32) = 6 + 0,(32) = 6 + 0,(01) . 32 = 6 + 1/99 . 32 = 6 + 32/99 = 626/99`

$g)$ `5,1(3) = 51,(3) : 10 = ( 51 + 0,(1) . 3 ) .1/10 = ( 51 + 1/9 . 3 ) . 1/10 = ( 51 + 1/3 ) . 1/10 = 154/3 . 1/10 = 1540/3`