Can a repeating decimal be equal to an integer?
No, it will allways turn out to be a fraction.
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):
The general term of a geometric series can be written:
#a_n = a*r^(n-1)#
#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#
In fact, any integer can be expressed as a repeating decimal using
#12345 = 12344.999... = 12344.bar(9)#
#-5 = -4.999... = -4.bar(9)#