Correct option is (A) 43/9
Let x = \(4.\bar{7}\)
\(\Rightarrow\) x = 4.777... ______(1)
Multiply equation (1) by 10, we obtain
10x = 47.777... ______(2)
Subtract equation (1) from (2), we get
10x - x = 47.777.... - 4.777....
\(\Rightarrow\) 9x = 43
\(\Rightarrow\) x = \(\frac{43}{9}\).