Question

express the number 0.123123123... in the form a/b where a and b are integers.

Answer 1

I simply did 123/999 do get me .0123123 it is in the a/b form and it is intergers however do i need to give anymore explanation or isthere some sort of special formula

Answer 2

ok, how did you get that, let's start there? lol

Answer 3

well Ijust tried 123/1000 first which gave me .123 not repeating and then i tried with 999 which has the repeating effect and got my a/b , trial and error lol

Answer 4

No need for trial and error:
\[\begin{align*}
x&=0.123123...\\
1000x&=123.123...\\
(1000-1)x&=123.123...-0.123123...\\
999x&=123\\
x&=\frac{123}{999}
\end{align*}\]

Answer 5

that works too

Answer 6

There's also a more tedious way of doing it with infinite series, but something tells me it might be excessive.