Just saw this post, and realized that
1/9801 = 0.00(010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979900)(repeat)
Similar properties are also exhibited by numbers 998001, 99980001, .. and so on.
It is not very obvious to me why this happens. Is there some simple explanation to this property?