Let's solve this question step by step.

Step 1: Decimal Representation of 5/27

To find the decimal representation of $\frac{5}{27}$, we perform the division: $\frac{5}{27} = 0.\overline{185}$ This means that the decimal representation of $\frac{5}{27}$ is a repeating decimal $0.185185185\ldots$ with a repeating block of "185."

Step 2: Determining the 50th Decimal Place

The repeating block "185" has 3 digits. To find the digit at the 50th decimal place, we need to determine the position within this repeating sequence:

1. Divide 50 by the length of the repeating sequence, which is 3: $50 \div 3 = 16 \text{ remainder } 2$
2. The remainder of 2 indicates that the 50th digit falls on the 2nd digit within the repeating block "185."

In "185", the second digit is 8.

Step 3: Thousandth’s Place

The repeating decimal $0.185$ places the digit "1" in the thousandth’s position since it falls directly in the first place of the repeating block.

Final Answers

1. 50th Digit: 8
2. Thousandth’s Place: 1

Would you like more details on how to tackle repeating decimals, or do you have further questions?

Here are five related questions for practice:

1. What is the 25th digit to the right of the decimal in the decimal representation of $\frac{5}{27}$?
2. If $\frac{7}{99} = 0.\overline{07}$, what is the 100th digit to the right of the decimal?
3. Determine the 10th digit in the repeating decimal of $\frac{3}{11}$.
4. Find the digit in the 20th place of the decimal expansion of $\frac{2}{7}$.
5. What digit is in the hundredth’s place of $\frac{4}{33}$?

Tip: When dealing with repeating decimals, find the repeating block and use modular arithmetic to locate specific digits in large positions.