https://file.aiquickdraw.com/mathbot/file/1728397871175opez9frx.jpg

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.

Determine the digit 50 places to the right of the decimal point in the decimal representation of 5/27. What digit is in the thousandth's place?

Find the 50th digit and the thousandth's place in the decimal representation of 5/27. Learn how to use modular arithmetic to identify specific positions in a repeating decimal sequence. Suitable for Grades 9-10 math learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation