# In 1/6=1.6666..., repeating 6 is called repeatend ( or reptend ) . I learn from https://en.wikipedia.org/wiki/Repeating_decimal, the reptend in the decimal form of 1/97 is a 96-digit string. Find fraction(s) having longer reptend string(s)?

##### 1 Answer

We can find the fraction for an arbitrary repeating string with the following method:

Let

So, for example, if we wanted a 1000-digit repeating string, we could let

give a repeating sequence of *any* repeating sequence.

If we let

would generate a a repeating string of the first

We can also use a similar method to find the fraction for *any* rational value with a repeating string.

Given a general real number with a repeating string

let

Note that by the above work, we have

Then we can rewrite our number as

#=c+b/10^k+a/(10^k(10^n-1))#

#=((10^kc+b)(10^n-1)+a)/(10^k(10^n-1))#