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

11 and 42 over 9999
11 and 42 over 9999
11 and 42 over 99
11 and 99 over 42

Question

Convert 11.42424242 … to a rational expression in the form of a over b, where b ≠ 0.

 11 and 42 over 9999
 11 and 42 over 9999
 11 and 42 over 99
 11 and 99 over 42

volleyballlover55 · Answer

@ijakez

anonymous · Answer

an easy example:$$0.12121212...=\frac{12}{99}$$

volleyballlover55 · Answer

ok sohow do we figure out this question?

anonymous · Answer

depends on your level of sophistication $$x=.121212...\
100x=12.121212...
99x=12\
x=\frac{12}{99}$$ is one method

anonymous · Answer

type there, i mean to write $$x=.121212...\
100x=12.121212...$$ subtract get 
$$99x=12\
x=\frac{12}{99}$$

anonymous · Answer

once you do one or two you will see instantly that for example $$0.4444...=\frac{4}{9}\
.121212...=\frac{12}{99}\
.123123123...=\frac{123}{999}$$ and so on

volleyballlover55 · Answer

so.. i got A

anonymous · Answer

definitely not A

anonymous · Answer

two numbers are repeating after the decimal
put them over 99

volleyballlover55 · Answer

ok

volleyballlover55 · Answer

i got C! :)