The decimal expression of the rational number `(23/(2^2 times 5))` will terminate after……….decimal place

Answer

To determine how many decimal places the decimal expression of the rational number \( \frac{23}{2^2 \times 5} \) will terminate after, we can follow these steps:

### Step 1: Identify the Denominator
The given rational number is:
\[ \frac{23}{2^2 \times 5} \]
Calculating the denominator:
\[ 2^2 = 4 \quad \text{and} \quad 5 = 5 \]
Thus, the denominator is:
\[ 2^2 \times 5 = 4 \times 5 = 20 \]

### Step 2: Write the Rational Number
Now, we can express the rational number as:
\[ \frac{23}{20} \]

### Step 3: Determine the Decimal Representation
To find the decimal representation of \( \frac{23}{20} \), we can perform the division:
\[ 23 \div 20 = 1.15 \]

### Step 4: Count the Decimal Places
The decimal representation \( 1.15 \) has two decimal places.

### Conclusion
Thus, the decimal expression of the rational number \( \frac{23}{2^2 \times 5} \) will terminate after **2 decimal places**.

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