After how many places of decimals will the decimal expansion of `(23457)/(2^(3) xx 5^(4))` terminate?

Answer

To determine after how many places of decimals the decimal expansion of \( \frac{23457}{2^3 \times 5^4} \) will terminate, we can follow these steps:

### Step 1: Identify the Denominator
We start with the denominator, which is \( 2^3 \times 5^4 \).

### Step 2: Determine the Values of \( m \) and \( n \)
In the expression \( 2^3 \times 5^4 \):
- \( m \) (the exponent of 2) is 3.
- \( n \) (the exponent of 5) is 4.

### Step 3: Compare \( m \) and \( n \)
Next, we compare the values of \( m \) and \( n \):
- \( m = 3 \)
- \( n = 4 \)

Since \( m < n \), the decimal expansion will terminate after \( n \) places.

### Step 4: Conclusion
Thus, the decimal expansion of \( \frac{23457}{2^3 \times 5^4} \) will terminate after **4 places of decimals**.

### Final Answer
The decimal expansion terminates after **4 places of decimals**.

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