One more cyclic number-16 digits

I had mentioned about cyclic number 142857 in my first blog.
Here is another example-a 16 digit number,starting (curiously you may think) with zero.
This number is the result of finding the reciprocal of 17,in which these16 digits occur in repetition,and obviously you can see that the first digit has to be zero.
The number is 05882352 94117647.
Let me give you a list of multiplicants which when used in multiplying this number give you new numbers where only the last righthandside digit moves to the front ,the remaining digits appearing in the same order in betwen.
Multiplication by 12.(M/12) gives                 70588235 29411764
M/8 -Multiplication by 8-gives you               47058823 52941176
M/11 gives you............................................64705882 35294117
M/13...........................................................76470588 23529411
M/3.............................................................17647058 82352941
M/2.............................................................11764705.88235294
M/7.............................................................41176470 58823529
M/16...........................................................94117647 05882352
M/5.............................................................29411764 70588235
M/9.............................................................52941176 47058823
M/6.............................................................35294117 64705882
M/4.............................................................23529411 76470588
M/14...........................................................82352941 17647058
M/15...........................................................88235294 11764705
M/10...........................................................58823529 41176470
You can see all the 16 multiplicants appear in the above list though not in the correct numerical order
You must be wondering what happens when you multiply with 17.You will get all sixteen of the digits as 9...........