Question

Plzzz telll me the solution of this question

Answer 1

Part I
Let
x=0.4272727....
hence
100x=42.7272727....
subtracting both equations
100x-x=42.7272727-0.42727...
99x=42.3
$x = \frac{42.3}{99}$
hence p/q form is
$\frac{423}{990}$

Part II
$\frac{5}{7} \\ = \frac{5}{7} \times \frac{11}{11} \\ = \frac{55}{77}$
$and \\ \frac{9}{11} \\ = \frac{9}{11} \times \frac{7}{7} \\ = \frac{63}{77}$

Hence three rational numbers between them are
$\frac{56}{77} ,\\ \frac{57}{77} ,\\ \frac{58}{77}$