Question 990665
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Hello,


do not be scared !   This phrase


{x|x is represented by a digit in the decimal expansion of 178/185} "


means 


"the set of those digits that participate in the decimal expansion of  {{{178/185}}} ".


The number  {{{178/185}}}  is rational,  SO its decimal expansion is either finite or periodic decimal fraction.  Are you familiar with it?


Next,  I performed long division of  178  by  185  for you.


It is the decimal fraction  0.9(621).


The three digits in parentheses are periodic part of the decimal expansion.


So,  the digits that participate in this decimal expansion of the number  {{{178/185}}}  are  1,  2  6  and  9.


Therefore,  our set is the set consisting of four digits  1,  2  6  and  9. 


Thus


{x|x is represented by a digit in the decimal expansion of 178/185} = {1, 2, 6, 9}.


THAT IS ALL.