Question

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

Answer 1

Let x = 0.424242... . Then 100x = 42.424242... . So we can write

100x - x = 99x = 42.424242... - 0.424242... = 42

which means

x = 42/99 = 14/33

and so

11.424242... = 11 + 14/33 = 377/33