Prime factors of the denominator of a rational number with the decimal expansion 25.2354 are:

Options

A. 2, 3
B. 2, 3, 5
C. 2, 7
D. 2, 5

Answer

To find the prime factors of the denominator of the rational number with the decimal expansion 25.2354, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Decimal to a Fraction:**
The decimal number 25.2354 can be expressed as a fraction:
\[ 25.2354 = \frac{252354}{10000} \]
Here, we move the decimal point 4 places to the right, which means we divide by \(10^4\) or 10000.

2. **Identify the Denominator:**
The denominator of the fraction is 10000.

3. **Find the Prime Factorization of 10000:**
We need to factor 10000 into its prime factors.
\[ 10000 = 10^4 \]
Since \(10 = 2 \times 5\), we can rewrite this as:
\[ 10000 = (2 \times 5)^4 = 2^4 \times 5^4 \]

4. **List the Prime Factors:**
The prime factors of 10000 are:
- \(2\)
- \(5\)

### Final Answer:
The prime factors of the denominator (10000) are \(2\) and \(5\).

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