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The question asks about a repeating decimal sequence: 
\[ 0,123454321123454321123454321\ldots \]
You are tasked with finding how many times the digit "4" appears in the first 200 digits after the decimal point.

### Pattern Analysis:
The given sequence appears to repeat in blocks of:
\[ 123454321 \]
This is a 9-digit repeating cycle, where the digit "4" appears twice in every cycle (positions 4 and 6).

### Steps to Solve:
1. **Determine full cycles within 200 digits:**
   - Each cycle has 9 digits.
   - Divide 200 by 9 to find how many full cycles fit: 
   \[ 200 \div 9 = 22 \text{ cycles} \text{ (remainder 2)} \]
   - So, 22 full cycles fit within the first 198 digits, and then we have 2 extra digits left to account for.

2. **Count the number of 4s in 22 full cycles:**
   - In each full cycle, "4" appears 2 times.
   - For 22 full cycles:
   \[ 22 \times 2 = 44 \text{ times} \]

3. **Check the remaining 2 digits:**
   - The first 2 digits of the sequence are "1" and "2," which do not contain the digit "4."

4. **Final Count:**
   - The total number of times "4" appears up to the 200th digit is \( 44 + 0 = 44 \).

### Answer:
The number of times the digit "4" appears in the first 200 digits is **44**.

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Would you like further details on this solution? Here are some related questions:

1. How would the answer change if the question asked for the first 300 digits instead?
2. How can you generalize the solution for any number of digits?
3. How would the pattern change if the sequence skipped some numbers, for example, skipping "3"?
4. How can this method be applied to other repeating decimal patterns?
5. What are other ways to detect patterns in repeating decimal sequences?

**Tip:** Always check how many digits are in the repeating block when analyzing repeating decimal patterns!

Perhatikan pola berikut! 0,123454321123454321123454321… Banyaknya angka 4 setelah tanda koma sampai urutan ke-200 adalah …. A. 44 B. 45 C. 46 D. 47

Analyze the repeating decimal sequence to determine how many times the digit '4' appears in the first 200 digits. Learn to identify patterns, perform division with remainders, and count specific digits within repeating cycles. Suitable for Grades 6-8 students.

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