Operations On Rational Numbers

The problem asks us to determine the number of decimal places after which the decimal expansion of the rational number will terminate.
A rational number will have a terminating decimal expansion if its denominator can be expressed in the form , where and are non-negative integers.

First, let's simplify the given expression:

Now, simplify :

The denominator is . Since it is in the form (and implicitly ), the decimal expansion will terminate.
The number of decimal places is determined by the largest power among and . Here, and .
Thus, there are 2 decimal places.

Therefore, the number of decimal places in the terminating decimal expansion of the rational number is 2.