rpt'ing decml to fraction

How do we write repeating decimals in fractional form? Answered by David Joyce Ph.D. in Mathematics, University of Pennsylvania 1979.
 
Case 1. The repetition begins immediately following the decimal point as in 0.142857142857142857. Typically, that is denoted with a bar over the repeating part with a repetition length of six. To write it as a fraction, use the six digits as a numerator and for the denominator use six nines.
 
142857/999999 = 1/7
 
Case 2. The repetition begins after a few digits as in 0.357142857. Convert the repeating part as described above and add that fraction into the non-repeating part. In this example the non-repeating part is 357/1000.

357 + 1/7 over 1000

That equals 2500/7000 = 5/14