Question

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

Answer 1

We have that 11.424242 ... = 11 + 0.424242 ...

Now let x = 0.424242 ...

Then 100x = 42.424242 ...

Now 99x = 100x - x = 42 so 99x = 42 and therefore x = 42/99

Now we can simplify 42/99 to 14/33

Now combining this we get 11.424242 ... = 11 + 14/33

= 363/33 + 14/33 = 377/33