1. decimal expansion

This is the problem, just wanting some help with it AND an explanation

There is a rule for the decmal expansion of 1/m, regardless of whether m is prime or not:

the number of digits in the repetenddivides the number of integers from 1 to m whose highest common factor with m is 1.

For example 1/21 = 0.047619 (recurring), the number of digits in the repetend is 6, and there are 12 integers from 1 to 21, whose highest common factor with 21 is 1: 1,2,4,5,8,10,11,13,16,17,19,20.

a) Check this rule for 1/51

b) find the family of fractions amongst n/51 for n = 1,2,3...,50, that have the same digits in their repetends as 1/51 but cyclically rotated.

c) Check the rule for all other families of fractions amongst n/51 for n = 1,2,3,...,50, that have the same digits in their repetends but cyclically rotated.

sry if this sounds a bit rude or something, but when you answer can you please put it in with working, and why, so i actually know how to do it...

Big thanks to whoever helps!

2. I replied to this in the original thread, sorry, that was at the same time you were trying to re-post it and move it.

3. Maybe this helps.