Given a number co-prime with 10, such as thirteen, we can construct a repeating decimal from its reciprocal: $\frac{1}{13}$ = 0.(076923). If we successively divide this number by a factor of 10 (i.e., 2 or 5) we get a sequence of numbers which have a fixed (non-repeating) and repeating portion (shown in parentheses):
$\frac{1}{26} = 0.0(384615)$
$\frac{1}{52} = 0.01(923076)$
$\frac{1}{104} = 0.009(615384)$
$\frac{1}{208} = 0.0048(076923)$
$\frac{1}{416} = 0.00240(384615)$
$\frac{1}{832} = 0.001201(923076)$
What is the correct terminology for the non-repeating and repeating portions of the decimals?
Given an eventually-periodic sequence, the piece occurring before the periodicity starts is called the preperiod (at least, this is the term I've always heard for it; note, however, that it might also be used to refer to the length of this piece). I don't know if there's a more specialized term for when we are talking about digits of a decimal expansion, but I think it's a good name for it regardless.