Rewrite as a simplified fraction.
3.2 = ? 2 is repeating

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

Step-by-step explanation:

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