Decimals 2

how funny the options are!

option-A:7 goes 7 times +more in 53.

option-B:4 goes 12 times +more in 50

option-C:6 goes 8 times + more in 51

and there remains only 1 option.

you could have done a little better with the options.

Convert $5.6666\dots$ into fraction

$0.6666\dots = \frac{6}{9}$ = $\frac{2}{3}$

$5 \frac{2}{3} = \boxed{\frac{51}{9}}$

$5.\dot { 6 } = \frac { 56 - 5 } { 9 } = \frac { 17 } { 3 }$ .

$\dfrac{51}{6} = 8.something\\ \dfrac{53}{7} = 7.something\\ \dfrac{50}{4} = 12.something\\ \dfrac{51}{9} = 5.something$

So, the only possible option is $\color{#69047E}{\boxed{\dfrac{51}{9}}}$ .

let $x=5.66...$ so $10x=56.66..$ when you subtract them we get $9x=51$ so $x=51/9$