Question

Number system .......​

Answer 1

$(i)$

$\tt \: x = 2.0 \bar { 15 }$

$\tt \: x = 2.01515....... \: \: \: \: \: \: \: \: \: \: \:$

$\tt \: multiplying \: 10 \: to \: both \: the \: sides \: of \: equation.$

$\tt \: x \times 10 = 2.0151515.... \times 10$

$\tt \: 10x = 20.1515.... \: \: \: \: \: \: \: \: \: \longrightarrow \red{eqn1}$

$\tt \: 20.1515 = 20. \bar{15}$

$\tt \: multiplying \: both \: sides \: by \: 100 \:$

$\tt \: \: 10x \times 100 = 20.1515... \times 100$

$1000x = 2015.1515.... \longrightarrow \: \: \: \orange{eqn2}$

${ \tt{ \bold {\blue{subtracting \: equarion \: (i )\: and \: (ii)}}}}$

$\tt \: 1000x - 10x = 2015.1515..... - 21.1515$

$\tt \: 990x = 1995$

$\tt \: x = \frac{ \cancel{1995}}{ \cancel{990}} = \frac{133}{66}$

${ \tt \purple{ \boxed{x = \frac{133}{66} }}}$