Let `x = 7/(20 xx25)` be a rational number . Then x has decimal expansion which terminates :

Answer

To determine if the rational number \( x = \frac{7}{20 \times 25} \) has a terminating decimal expansion, we can follow these steps:

### Step 1: Simplify the expression for \( x \)
We start with the expression:
\[ x = \frac{7}{20 \times 25} \]
First, we calculate \( 20 \times 25 \):
\[ 20 \times 25 = 500 \]
So, we can rewrite \( x \) as:
\[ x = \frac{7}{500} \]

### Step 2: Factor the denominator
Next, we factor the denominator \( 500 \):
\[ 500 = 5^3 \times 2^2 \]
This means:
\[ x = \frac{7}{5^3 \times 2^2} \]

### Step 3: Check the prime factors of the denominator
For a rational number to have a terminating decimal expansion, its denominator (in simplest form) must only have the prime factors 2 and/or 5. Here, the denominator \( 500 \) consists of the prime factors \( 5 \) and \( 2 \), which satisfies the condition.

### Step 4: Convert to decimal
Now, we can convert \( x \) to decimal:
\[ x = \frac{7}{500} = 7 \div 500 \]
Performing the division:
\[ 7 \div 500 = 0.014 \]

### Conclusion
Thus, the decimal expansion of \( x \) is \( 0.014 \), which terminates after 3 decimal places.

### Final Answer
The decimal expansion of \( x \) terminates after 3 digits.

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