What is, the 25th digit to the right of the decimal point in the decimal of `(6)/(11)` ?

Options

A. 5
B. 3
C. 4
D. 6

Answer

To find the 25th digit to the right of the decimal point in the decimal representation of \( \frac{6}{11} \), we can follow these steps:

### Step 1: Calculate the decimal representation of \( \frac{6}{11} \)

To convert \( \frac{6}{11} \) into a decimal, we perform the division:

\[ 6 \div 11 = 0.54545454\ldots \]

This shows that the decimal representation is \( 0.\overline{54} \), which means it is a repeating decimal with the digits "54" repeating indefinitely.

### Step 2: Identify the pattern in the decimal

The repeating part of the decimal is "54". This means every two digits, the sequence repeats:

- 1st digit: 5
- 2nd digit: 4
- 3rd digit: 5
- 4th digit: 4
- 5th digit: 5
- 6th digit: 4
- ...

### Step 3: Determine the position of the 25th digit

Since the decimal repeats every 2 digits, we can find the position of the 25th digit by calculating:

\[ 25 \mod 2 \]

Calculating this gives us:

\[ 25 \mod 2 = 1 \]

This means that the 25th digit corresponds to the 1st digit in the repeating sequence "54".

### Step 4: Find the digit

From our earlier identification of the repeating pattern:

- The 1st digit is 5
- The 2nd digit is 4

Thus, the 25th digit to the right of the decimal point in the decimal representation of \( \frac{6}{11} \) is **5**.

### Final Answer:
The 25th digit to the right of the decimal point in the decimal of \( \frac{6}{11} \) is **5**.

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