11.424242
isolate the repeating part
11+0.424242
focus on the repeating part
0.42424242
how many places till it repeats again?
2
let's say it is x
x=0.42424242
multiply by 100
100x=42.424242
subtract them
100x-x=42.42424242-0.42424242
the infinite repeats cancel and we get
99x=42
divide by 99
[tex]x=\frac{42}{99}[/tex]
so
[tex]11.\overline{42}=11 \space\ \frac{42}{99}[/tex]
