The question asks to determine two things about the decimal representation of the fraction $\frac{5}{27}$:

1. Determine the digit 50 places to the right of the decimal point.
2. Which of the following digits is not repeated in the decimal representation?

Step 1: Find the Decimal Representation of $\frac{5}{27}$

We begin by dividing 5 by 27: $\frac{5}{27} = 0.\overline{185}$ This means the decimal representation is repeating with the sequence "185" infinitely.

Step 2: Finding the 50th Digit

Since the decimal repeats every 3 digits ("185"), we need to determine the position of the 50th digit within the repeating sequence. We do this by finding the remainder when 50 is divided by 3: $50 \div 3 = 16 \text{ remainder } 2$ This means that the 50th digit corresponds to the 2nd digit in the repeating sequence "185". Therefore, the 50th digit is 8.

Step 3: Which Digit Is Not Repeated?

The repeating sequence is "185". The digits that repeat are 1, 8, and 5. Out of the given options (8, 1, 5, 0), the digit 0 is not present in the repeating sequence.

Final Answers:

1. The digit 50 places to the right of the decimal point is 8.
2. The digit that is not repeated in the decimal representation is 0.

Would you like further clarification on any part of this solution? Here are some follow-up questions to deepen understanding:

1. How can you verify the decimal expansion of other fractions like $\frac{5}{27}$?
2. Why does the decimal of $\frac{5}{27}$ repeat after 3 digits?
3. How would the result change if the fraction were $\frac{5}{26}$?
4. What is the pattern in determining the digit at any position in a repeating decimal?
5. How can repeating decimals be converted back into fractions?

Tip: When working with repeating decimals, finding the length of the repeating cycle is key to solving problems involving specific digits in the expansion.