Without actual performing the long division fine if `395/10500` will have terminating or non terminating (repeating decimal expansion).

Answer

To determine whether the fraction \( \frac{395}{10500} \) has a terminating or non-terminating decimal expansion, we need to analyze the prime factorization of the denominator, \( 10500 \).

### Step-by-Step Solution:

1. **Factor the Denominator**: Start by finding the prime factorization of \( 10500 \).
- Divide \( 10500 \) by \( 2 \) (the smallest prime number):
\[ 10500 \div 2 = 5250 \]
- Divide \( 5250 \) by \( 2 \):
\[ 5250 \div 2 = 2625 \]
- Now, \( 2625 \) is not divisible by \( 2 \). Next, divide by \( 3 \):
\[ 2625 \div 3 = 875 \]
- Now, divide \( 875 \) by \( 5 \):
\[ 875 \div 5 = 175 \]
- Divide \( 175 \) by \( 5 \):
\[ 175 \div 5 = 35 \]
- Finally, divide \( 35 \) by \( 5 \):
\[ 35 \div 5 = 7 \]
- The last number, \( 7 \), is a prime number.

2. **Write the Prime Factorization**: Now we can write the complete prime factorization of \( 10500 \):
\[ 10500 = 2^2 \times 3^1 \times 5^3 \times 7^1 \]

3. **Check for Terminating Decimal Condition**: A fraction has a terminating decimal expansion if, after simplification, the denominator has no prime factors other than \( 2 \) and \( 5 \).
- In our factorization, we see that \( 10500 \) contains the prime factors \( 3 \) and \( 7 \) in addition to \( 2 \) and \( 5 \).

4. **Conclusion**: Since the denominator \( 10500 \) has prime factors other than \( 2 \) and \( 5 \), specifically \( 3 \) and \( 7 \), the fraction \( \frac{395}{10500} \) will have a non-terminating decimal expansion.

### Final Answer:
The decimal expansion of \( \frac{395}{10500} \) is non-terminating.

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