SOLUTION: Hi, I'm having trouble understanding this particular question about sets. Was wondering if someone could explain to me what it means. {x|x is represented by a digit in the de

Question 990665: Hi,
I'm having trouble understanding this particular question about sets. Was wondering if someone could explain to me what it means.
{x|x is represented by a digit in the decimal expansion of 178/185}
I don't know what is being asked.
Thanks
Answer by ikleyn(52839)   (Show Source): You can put this solution on YOUR website!
.
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 ".

The number    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 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.

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