Without actual division, show that each of the rational numbers given below is expressible as a terminating decimal :
`17/20`

Answer

To determine whether the rational number \( \frac{17}{20} \) is expressible as a terminating decimal without performing the actual division, we can analyze the denominator.

### Step-by-step Solution:

1. **Identify the Denominator**:
The denominator of the given rational number is 20.

2. **Factor the Denominator**:
We need to express 20 as a product of its prime factors.
\[ 20 = 2^2 \times 5^1 \]

3. **Check the Form of the Denominator**:
A rational number can be expressed as a terminating decimal if its denominator (after simplification) can be expressed in the form \( 2^m \times 5^n \), where \( m \) and \( n \) are non-negative integers.

4. **Analyze the Factors**:
From our factorization, we see that:
\[ 20 = 2^2 \times 5^1 \]
Here, \( m = 2 \) and \( n = 1 \), both of which are non-negative integers.

5. **Conclusion**:
Since the denominator 20 can be expressed in the form \( 2^m \times 5^n \), we conclude that \( \frac{17}{20} \) is expressible as a terminating decimal.

### Final Statement:
Thus, \( \frac{17}{20} \) is a terminating decimal.

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