# Using https://socratic.org/questions/in-1-6-1-6666-repeating-6-is-called-repeatend-or-reptend-i-learn-from-https-en-w, how do you design a set of rational numbers { x } that have reptend with million digits?

Sente provided the theory in his response.

For a portion of the response

denotes the least important number.

Clarification:

all of the ds are 0.

Next.

#=2.209 7000...0003 7000...0003 7000...0003 ... ad infinitum.

The number of sd in the numerator and denominator is the same.

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See below.

Warning: The following is highly generalized and contains some atypical constructions. It may be confusing for students not completely comfortable with constructing sets.

Now we can make our set of repetends.

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To design a set of rational numbers with a reptend consisting of a million digits, you can use the repeating decimal representation. One way to do this is by choosing the repeating digit as 6, and the non-repeating part as 0. This will give you the rational number 0.666... (with a reptend of million 6s).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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