Yes, any decimal representation of a number with repeating digits after the decimal point is a rational number, though which fraction the given number represents depends on which block of digits is repeating.
For example, if the given number is
x = 0.347213472134721…
with (34721) as the repeating block, then
10⁵ x = 34721.347213472134721…
so that
10⁵ x - x = 34721.347213472134721… - 0.347213472134721…
(10⁵ - 1) x = 34721
x = 34721 / (10⁵ - 1) = 34721/99999
Or, if (4721) is the repeating block, then
x = 0.3472147214721…
10x = 3.472147214721…
10⁵ x = 34721.472147214721…
10⁵ x - 10x = 34721.472147214721… - 3.472147214721…
(10⁵ - 10) x = 34718
x = 34718 / (10⁵ - 10) = 17359/49995
Or, if (721) is the repeating block, then
x = 0.34721721721…
10² x = 34.721721721…
10⁵ x = 34721.721721721…
10⁵ x - 10² x = 34721.721721721… - 34.721721721…
(10⁵ - 10²) x = 34687
x = 34687 / (10⁵ - 10²) = 34687/99900
Hopefully you get the idea.
