Just saw this post, and realized that
1/9801 = 0.(000102030405060708091011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192939495969799)(repeat)
Similar properties are also exhibited by numbers 998001, 99980001, .. and so on.
Edit: fixed periodic start and end
It is not very obvious to me why this happens. Is there some simple explanation to this property?