# Can a repeating decimal be equal to an integer?

##### 2 Answers

No, it will allways turn out to be a fraction.

#### Explanation:

I will not delve into how you turn a repeating decimal into a fraction, but just one example:

There is **one exeption** though (see example above):

Yes

#### Explanation:

The general term of a geometric series can be written:

#a_n = a*r^(n-1)#

where

When

#sum_(n=1)^oo ar^(n-1) = a/(1-r)#

So for example:

#0.999... = 9/10+9/100+9/1000+...#

is given by

which has sum:

#sum_(n=1)^oo 9/10*(1/10)^(n-1) = (9/10)/(1-1/10) = (9/10)/(9/10) = 1#

So

In fact, any integer can be expressed as a repeating decimal using

For example:

#12345 = 12344.999... = 12344.bar(9)#

#-5 = -4.999... = -4.bar(9)#