Question

express 5.3bar in the form of p\q where p & q are integers q is not equal to 0

Answer 1

5.3=53/10
this is the answer

Answer 2

To express 5.3bar into a form of p/q following the given circumstances,

$let \: x = 5.333.... \\ = > x = 5.33... \: \: \: \: \: \: \: \: \: \: \: \: eqn \: 1 \\ = > 10x = 53.33... \: \: \: \: \: eqn2 \\ now \: subtracting \: eqn \: 1 \: from \: 2 \\ we \: get: \\ 10x - x = (53.33...) - (5.33...) \\ = > 9x = 48 \\ = > x = \frac{48}{9} = \frac{16}{3} \\ to \: check \: the \: answer \\ \frac{16}{3} = 5.33...$