Question

Convert 11.42424242 … to a rational expression in the form of a over b, where b ≠ 0.

Answer 1

$x = 11\frac{42}{99}$

Step-by-step explanation:

$11.42424242.... = 11. \overline{42} \\ let \: x = 11. \overline{42} .....(1)\\ 100x = 1142.\overline{42}....(2) \\ subtracting \: (1) \: from \: (2) \: \\ 100x - x = 1142.\overline{42} - 11. \overline{42} \\ 99x = 1131 \\ x = \frac{1131}{99} \\x = 11\frac{42}{99}$