Answer:
3
.
¯
2
=
29
9
Explanation:
Using the notation of a bar over a set of digits to denote their infinite repetition,
let
x
=
3
.
¯
2
⇒
10
x
=
32
.
¯
2
⇒
10
x
−
x
=
32
.
¯
2
−
3
.
¯
2
=
29
⇒
9
x
=
29
∴
x
=
29
9
This technique works in general. Set
x
as your desired value, multiply by
10
n
where
n
is the number of digits repeating, and then subtract
x
to eliminate the infinitely repeating portion. It then is just a matter of dividing by
10
n
−
1
a
Explanation: