The decimal expansion for the rational number (11 / (2^3 * 5^2)) will terminate after: A) One decimal place B) Two decimal places C) Three decimal places D) More than 3 decimal places

To determine the number of decimal places after the decimal expansion of the rational number \(\dfrac{11}{2^3 \cdot 5^2}\), we need to examine the prime factorization of the denominator and check if the decimal expansion will terminate.

1. **Prime factorization of the denominator:**
The denominator is \(2^3 \cdot 5^2\).
We have two prime factors: 2 and 5, both of which are the prime factors of 10.

2. **Condition for termination of the decimal expansion:**
A rational number has a terminating decimal expansion if and only if the denominator (when the fraction is in its simplest form) has no prime factors other than 2 and 5.

3. **Simplifying the expression:**
The denominator is \(2^3 \cdot 5^2\), which is already in the form of prime factors of 2 and 5.

4. **Number of decimal places:**
For the decimal expansion to terminate, we can convert the denominator into powers of 10 by multiplying the numerator and denominator by appropriate powers of 2 or 5. The number of decimal places corresponds to how many powers of 10 are in the denominator after simplification.

The denominator \(2^3 \cdot 5^2 = 8 \cdot 25 = 200\).

5. **Now calculate the decimal:**
\[
\dfrac{11}{200} = 0.055
\]

The decimal expansion is \(0.055\), which terminates after **three decimal places**.

Thus, the correct answer is:

**C) Three decimal places**.